p ( )URL: http://www.elsevier.nl/locate/entcs/volume51.html 64 pages

GETGRATS: A summary of scienti�c results(with annotated bibliography)

Edited by: Andrea Corradini 1

Dipartimento di Informatica

Universit�a di Pisa

Pisa, Italy

Abstract

This document summarizes the main scienti�c contributions of the research activity

carried within the GETGRATS project during the lifetime of the network (from

September 1, 1996, till August 31, 2001).

The bibliography lists about 300 publications, most of which in international

journals or conferences. Backward links from the bibliography items to the body of

the document allow one to use it as an annotated bibliography.

Contents

1 Introduction 2

2 Theory of the basic approaches to graph rewriting 5

2.1 Algebraic Approaches: Single and Double Pushout 5

2.2 Pullback rewriting 6

2.3 Hyperedge Replacement and Vertex Replacement 6

2.4 High-level Replacement Systems 7

2.5 Algebra Transformation Systems 8

2.6 Tree Transducers 9

2.7 2-Structures 10

2.8 Deterministic Push-Down Automata 10

2.9 Programming constructs for graph transformation based

languages 11

2.10 Graph-Theoretical results 11

3 Speci�cation 11

3.1 Speci�cation of Open and Reactive Systems with Graph

Transitions and Views 11

1Email: andrea@di.unipi.it

c 2002 Published by Elsevier Science B. V.Open access under CC BY-NC-ND license.

Corradini

3.2 Modelling of Open Systems using Tiles 13

3.3 Speci�cation of graph properties by Monadic Second Order

Logic 14

3.4 Modal and Temporal Logics for Graph Transformation 16

3.5 Integration of Data and Behavioural Speci�cation Formalisms 17

3.6 Other approaches: Coupled Graph Grammars and Graphical

SOS. 17

4 Structuring aspects 18

4.1 Distributed Graph Transformation 18

4.2 Software Architecture 20

4.3 Hierarchical Graphs 21

4.4 Modularity Concepts: GRACE and Transformation Units 22

4.5 Modules for Typed Graph Transformation Systems and

Re�nement Relations 23

4.6 Colimit constructions 24

5 Semantics 24

5.1 Concurrent Semantics of Algebraic Graph Grammars 24

5.2 Local Action Systems: Process semantics and Modelling of

Petri Nets 26

5.3 Categorical representation of Term Graphs and applications 28

5.4 Inductive de�nition of graph transformation 30

5.5 Coalgebraic Semantics of Structured Transition Systems 30

5.6 Algebraic semantics of (contextual) Petri nets 31

6 Applications 32

6.1 Term Graph Rewriting and Term Graph Narrowing 32

6.2 DNA Computing 33

6.3 Collage Grammars and Picture Generation 34

6.4 Modelling of Mobile Ambients 35

6.5 Modelling of Agent Based Systems 35

6.6 Speci�cation of Control Access Policies 36

6.7 Management of semi-structured data and Hypermedia

Modeling 36

6.8 Graph Matching 36

7 Distributed Algorithms based on Graph Relabeling Systems 37

8 Handbooks, Tutorials, and Proceedings 39

References 40

1 Introduction

GETGRATS (General Theory of Graph Transformation Systems) was a Re-

search TMR Network funded by the European Commission for �ve years, from

September 1, 1996, till August 31, 2001. GETGRATS was formed by seven

2

Corradini

research groups, as listed here together with the corresponding team leaders:

(i) University of Antwerp (Belgium): Prof. Dr. Dirk Janssens

(ii) Technische Universit�at Berlin (Germany): Prof. Dr. Hartmut Ehrig

(iii) Laboratoire Bordelais de Recherche en Informatique (France): Prof. Dr.

Michel Bauderon

(iv) Universit�at Bremen (Germany): Prof. Dr. Hans-Joerg Kreowski

(v) University of Leiden (The Netherlands): Prof. Dr. Grzegorz Rozenberg

(vi) Universit�a di Pisa (Italy) [main contractor]: Prof. Ugo Montanari

(vii) Universit�a di Roma La Sapienza (Italy): Prof. Dr. Francesco Parisi

Presicce

The Network Coordinator was Andrea Corradini (Universit�a di Pisa, Italy).

The present document describes the main scienti�c contributions of the

research activity carried within the GETGRATS project during the lifetime

of the network, and it includes a bibliography listing about 300 publications

by the GETGRATS members, most of which in international journals and

conferences.

According to the Project Programme of GETGRATS, \the aim of this

project is to develop a General Theory of Graph Transformation Systems

by solidifying the use of mathematics in their study and regarding them as

the objects of discourse and interest." The research themes addressed in the

project were divided into the following seven \focus areas":

(a) Foundation, Uni�cation, Combination and Comparison, concerning the

comparison and uni�cation of di�erent approaches to graph rewriting, or

speci�c aspects of such approaches.

(b) Classi�cation and Expressive Power, including the identi�cation of various

structural properties of GTS that have e�ect on the expressive power.

(c) Analysis and Veri�cation Techniques, concerning the development of anal-

ysis and veri�cation techniques to study which properties of the semantics

can be deduced or decided by inspecting the syntactic descriptions of GTS.

(d) Abstract Semantics, including investigation of semantics based on deriva-

tion sequences (abstract or concrete), processes and event structures, espe-

cially in the light of research about modularity and concurrency.

(e) Concurrency Aspects, concerning the development of concepts of concur-

rent and distributed GTS including appropriate semantics, as well as their

comparison to other models for concurrency.

(f) Modularity Aspects, including the de�nition of module concepts, borrowing

techniques from other areas like abstract data types.

(g) Morphisms, Transformations and Operations, including the de�nition of

suitable categories of graph processes, event structures and other abstract

domains, and to relate them with categories of grammars through functors,

3

Corradini

or, better, through adjunctions.

This division was intended to facilitate to focus (and hence to intensify) the

cooperation between the various partners. However, in order to describe the

research activity done in the network to non-specialists of the area, it turns

out to be more convenient to structure the presentation according to main

research themes. In particular, the various contributions can be (loosely)

classi�ed under the following headlines:

(i) Theory of the basic approaches to graph rewriting , concerning the def-

inition and the study of the properties of various approaches, includ-

ing the Algebraic Approaches, Pullback rewriting, Hyperedge and Vertex

Replacement, High-level Replacement Systems, Algebra Transformation

Systems, Tree Transducers, and 2-Structures, among others.

(ii) Speci�cation techniques based on graph transformation systems, includ-

ing the speci�cation of Open and Reactive Systems with Graph Transi-

tions, Views, and Tiles; the Speci�cation of graph properties by Monadic

Second Order Logic; Modal and Temporal Logics for GTSs; and the In-

tegration of Data and Behavioural Speci�cation Formalisms.

(iii) Structuring aspects, including the structuring of systems in the spatial

dimension (as in Distributed Graph Transformations and Hierarchical

Graph Transformations), and the logical structuring of systems from a

Software Engineering perspective (like in the GTS-based approaches to

Software Architectures, Modularity, and Re�nement).

(iv) Semantics of graph transformation systems, including process-based (con-

current) semantics for Algebraic Graph Grammars and Local Action Sys-

tems; Unfolding, Event-based and Abstract Semantics (using Bisimula-

tion) of Algebraic Graph Grammars; the Categorical Representation of

Term-like Structure and its application to Term Graph Rewriting; the In-

ductive De�nition of GTS's; Coalgebraic Semantics of Structured Tran-

sition Systems; and the Algebraic semantics of (contextual) Petri nets.

(v) Applications, concerning the use of one or more of the basic approaches

to main case studies, like the graphical representation of terms and of

rewriting rules (Term Graph Rewriting and Narrowing); the modeling of

gene assembly in ciliates in DNA Computing; graphical applications like

Collage Grammars and Picture Generation; modeling of Mobile Ambients

and Agent Based Systems; Speci�cation of Access Control Policies; and

others.

(vi) Distributed Algorithms based on Graph Relabelling Systems, used to

model local computations on graphs; among others, three classical prob-

lems are addressed: the recognition problem, the election problem and

the termination detection problem.

(vii) Handbooks, Tutorials and Conference Proceedings. Under this headline

we will list a number of publications which are either tutorial introduc-

4

Corradini

tions to the various approaches to graph transformation systems, or sur-

veys of results in speci�c research areas. Such contributions witness the

e�orts of the members of the network in training activities.

In the following sections for each of the above headlines we will describe brie y

the main topics and contributions worked out during GETGRATS.

2 Theory of the basic approaches to graph rewriting

2.1 Algebraic Approaches: Single and Double Pushout

In [HMP00], three variants of the classical double-pushout approach ([CMR+97])

to graph transformation are obtained by considering injective matching and/or

arbitrary right-hand morphisms in rules. It is shown that, compared with the

traditional approach with arbitrary matching, injective matching provides ad-

ditional expressiveness for both generating graph languages by grammars with-

out non-terminals, and for computing graph functions by convergent graph

transformation systems. Moreover, for the most general variant with injec-

tive matching and arbitrary right-hand morphisms, sequential and parallel

commutativity is established by strengthening sequential and parallel inde-

pendence. Additionally, in [HMP01] the classical theorems on parallelism and

concurrency are adapted to the setting with injective matching.

In [Plu98] it is shown that termination is an undecidable property of graph

rewriting systems (in the double-pushout approach). The proof is by a reduc-

tion of the Post Correspondence Problem. It is also argued that neither the

halting problem for Turing machines nor the termination problem for string

rewriting systems can be reduced to the termination problem for graph rewrit-

ing in a straightforward way.

In [BMRV99] the single-pushout approach ([EHK+97]) is extended to the

algebraic transformation of partial many-sorted unary algebras. The main re-

sult is an algebraic characterization of the single-pushout transformation in the

categories of all conformisms, all closed quomorphisms, and all closed-domain

closed quomorphisms of unary partial algebras over a given signature, together

with a corresponding operational characterization. Another important result

is the de�nition of high-level replacement conditions for amalgamation, and

the three mentioned categories are shown to satisfy all the high-level replace-

ment conditions for parallelism and amalgamation.

In [Gru00b] the typed SPO-approach has been extended by meta-typing

facilities. The main result is that the presented concept of meta-typing is

compatible with the SPO theory and can be implemented into the SPO-based

graph grammar environment AGG without spoiling its formal basis. This

SPO-based approach to meta-typing is compared with the algorithmic ap-

proach to meta-typing followed in PROGRES.

5

Corradini

2.2 Pullback rewriting

Pullback rewriting [BJ01b] was proposed recently as a categorical framework

to describe vertex replacement in graphs. Since then it has appeared as a

fairly powerful mechanism to describe a large number of graph rewriting sys-

tems. In particular, it is shown in [BJ01a] how this could be used to provide

a uniform rewriting mechanism for a wide class of graphs which are uniformly

described under the name of \structured graphs". Pullback rewriting is ap-

plied in [Kle98] to describe Petri net re�nements and in [JK00] to implement

NCE node rewriting in hypergraphs.

Pullback rewriting may be considered also as a (de)composition mecha-

nism. In this approach, it is shown in [BC00] how some types of graphs may

be decomposed in two \orthogonal components", whose pullback is the origi-

nal graph. Iterating the process, these graphs may be written as a composition

of some basic buildings blocks. This result gives an easy description of several

types of graphs who look very regular (like grids), although there are not so,

in any language theoretic sense.

The elaboration of a complete and adequate framework for pullback rewrit-

ing has been continued, leading to the presentation of H�el�ene Jacquet's Ph.D.

thesis in January 1999. In the survey [BJK02] on the pullback approach to

graph rewriting, the basic mechanism with extensions to parallel rewriting

as well as applications to NLC rewriting and re�nement of Petri nets are

described.

2.3 Hyperedge Replacement and Vertex Replacement

In [Dre97,Dre98a] the structure of Hyperedge Replacement (HR) graph lan-

guages consisting of (hyper)trees is investigated. It is shown that these lan-

guages can be generated by productions whose right-hand sides are themselves

hypertrees. However, for this, the sets of derivation trees have to be produced

by a �nite-copying top-down tree transducer. Thus, �nite copying compen-

sates the loss in power that results from allowing only hypertrees as right-hand

sides.

In [Man98] the concept of cooperation and distribution as known from the

area of grammar systems is introduced to graph grammars, more precisely,

to Hyperedge Replacement grammars. Two di�erent derivation modes are

considered, the so-called t-mode and the = k-mode. For the t-mode it is

shown that the class of hypergraph languages obtained is equal to the class of

ET0L HR languages which are a natural generalization of the ET0L languages

to hypergraphs.

In [CM00], a common framework for HR and Vertex Replacement (VR)

context-free graph and hypergraph grammars is presented, based on hyper-

graph operations de�ned by quanti�er free formulas and also on the fusion of

all vertices with same label. Concerning graph decompositions based on graph

operations de�ning VR grammars, the corresponding complexity measure is

6

Corradini

called clique-width. The case of in�nite graphs raises speci�c problems. In

[HK98], atom replacement in hypergraphs is introduced which combines and

uni�es the concepts of node replacement and hyperedge replacement.

In [DK01b] hyperedge replacement languages are viewed as syntax dia-

grams. By reading the labels of edges along a path, a word is obtained. The

article investigates this speci�cation method for string languages in particular

with respect to its generative power.

Con uent node-rewriting graph grammars, which are called C-edNCE gram-

mars in the literature, are known to provide the most powerful context-free

approach to graph rewriting with respect to generative power. Considering

the context-free rewriting of hypergraphs instead of graphs, it is shown in

[Kle99] that con uent node rewriting allows to specify all hyperedge-rewriting

and separated handle-rewriting languages, and even languages beyond that

union. Still, there are some normal forms for these C-hNCE grammars which

allow to deduce that the generated graph languages can already be speci�ed

by C-edNCE grammars [Kle01]. A comprehensive study of context-free hyper-

graph grammars with node and hyperedge rewriting is presented in Klempien-

Hinrichs' doctoral thesis [Kle00], including an application to the re�nement of

Petri nets. Some major results of the thesis are brie y summarized in [Kle02].

Attributed context-free hypergraph grammars (acfhg grammars) are intro-

duced in [MV98]. Acfhg grammars and attribute grammars are closely related:

an attribute grammar can be used to compute the attribute values of an acfhg

grammar. Several known formalisms, such as compatible functions and at-

tributed tree grammars can be embedded into acfhg grammars. An acfhg

grammar can be used to de�ne the semantics of a programming language P

in such a way that non-context-free constraints of P are already checked in

the syntactical phase, i.e., by the underlying graph grammar.

2.4 High-level Replacement Systems

High-level Replacement Systems are an axiomatic categorical framework which

has been introduced to generalize the concept of graph transformation systems

and graph grammars from graphs to many kinds of structures which are of

interest in Computer Science andMathematics. Within the algebraic approach

to graph transformation this is possible by replacing graphs, graph morphisms,

and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a

suitable category. Of special interest are categories for all kinds of labelled

and typed graphs, hypergraphs, algebraic speci�cations and Petri nets.

In [Tae97], Parallel High-level Replacement systems are introduced to for-

malize within this framework the notion of parallel rewriting. On the one

hand this concept generalizes and extends parallel graph grammars presented

so far in the algebraic approach by allowing other structures than graphs,

on the other hand the kinds of replacement introduced for high-level replace-

ment systems are extended by di�erent types of parallel replacement which

7

Corradini

are compared to each other in di�erent theorems. An abstract version of a

window-based graph editor and the description of the movement of objects in

con�guration spaces are presented as examples of parallel high-level replace-

ment systems.

The main theoretical concepts and results of high-level replacement sys-

tems are surveyed in [EGP99], where it is shown how some basic results for

graph transformation systems in the algebraic double pushout approach can

be reformulated in this more general framework. The speci�c choice of re-

sults concerning local Church-Rosser properties and horizontal structuring is

motivated by the results needed in the application domains studied in this

contribution, which include algebraic speci�cations and Petri nets, where a

transformation corresponds to a rule-based change of the structure of the spec-

i�cation or of the net, respectively. A recent survey of the theory of high-level

replacement systems is presented in [EHP02].

In [Pad99] several results for high-level replacement systems are presented,

centered around a categorical notion of re�nement which is called Q-transformation.

Several concepts and results of high-level replacement systems are extended to

Q-transformations. These are sequential and parallel transformations, union,

and fusion, based on di�erent colimit constructions. These results are applied

in [Pad99], [PGE98] and in [PG98] to Petri nets.

System veri�cation in the broadest sense deals with those semantic prop-

erties that can be decided or deduced by analyzing a syntactical description

of the system. In [KV00] the semantic properties of redundancy and sub-

sumption are carried over from rule-based systems to high-level replacement

systems, which in turn generalize graph and hypergraph grammars. The main

results are a characteriztion of subsumption and a suÆcient condition for re-

dundancy, which involves composite productions.

2.5 Algebra Transformation Systems

Algebra Transformation Systems are introduced as formal models of compo-

nents of open distributed systems in [Gro98]. They are given by a transition

graph modelling the control ow, and by partial algebras and method ex-

pressions, modelling the data states and their transformations. According

to this two{level structure they cover both labelled transition systems and

rule based speci�cation approaches, corresponding to information, computa-

tion and engineering viewpoint models. Di�erent composition operations for

algebra transformation systems are investigated. Limits and colimits model

parallel and sequential composition of components, signature morphisms yield

appropriate syntactical support for such compositions. The most important

compositionality properties known from algebraic speci�cation, like colimits of

signatures and amalgamation of models, also hold for the framework of alge-

bra transformation systems. The relevant, technical problem of constructing

pushout complements in the case of partial algebras is addressed in [LR00].

8

Corradini

In [Gro02], composition operations and re�nement relations have been de-

�ned for algebra transformation systems so that a semantical level for the

composition of system components is de�ned. The de�nition of re�nement

relations, also on the semantical level, supports the iterative development

of more concrete design speci�cations from more abstract design or require-

ment speci�cations. Both composition operations and re�nement relations

are treated abstractly as schemes and can be instantiated di�erently to obtain

concrete composition operations and re�nement relations, respectively. These

schemes are de�ned categorically.

2.6 Tree Transducers

In [DE98] the �niteness of ranges of a large class of tree transductions is

proved to be decidable. It is shown that this yields a generalization of known

decidability results concerning boundedness problems for functions on graphs

and other domains. The functions that can be dealt with are de�nable by

recursion on the derivation tree of a graph.

In [EV98] it is shown that bottom-up and top-down tree-to-graph trans-

ducers de�ne the same class of tree transductions (as opposed to the classical

bottom-up and top-down tree transducers).

In [BE00] and [EM99] a comparison is made between MSO de�nable tree

transductions, i.e., tree transductions that can be speci�ed in monadic sec-

ond order logic, and classical, implementation-oriented tree transduction for-

malisms: attribute grammars and functional programming. It is shown in

[BE00] that MSO de�nable tree transductions correspond to \single use" at-

tribute grammars, and in [EM99] that they correspond to \�nite copying"

macro tree transducers. These results can be viewed as the generalization

to tree translations of B�uchi's classical result that MSO de�nable string lan-

guages correspond to �nite automata.

In [EM00b] a characterization is given of the class of tree languages which

can be generated by context-free hyperedge replacement graph grammars, in

terms of macro tree transducers: it is the class of output tree languages of

macro tree transducers which are �nite copying and special in the parameters

(that is, linear and nondeleting).

There is a close relationship between graph grammars and tree transducers.

In [Man99] the class of string languages that can be generated by macro tree

transducers (MTTs) is considered. Via a `bridge-theorem' it is shown that

total deterministic MTTs cannot generate particular languages generated by

much simpler, nondeterministic devices (namely, ET0L systems). In [MN99]

it is shown that the eXtensible Style sheet Language XSL, commonly used to

transform XML code into HTML code, can be modeled by certain top-down

tree transducers. The essential new point is that these transducers operate on

unranked trees. Another characterization of this class by means of monadic

second-order logic is given, and various complexity results are proved.

9

Corradini

It is well known that context-free graph languages can be obtained from

regular tree languages by means of MSO-de�nable tree-to-graph transductions.

In [EM00a,EM01] the MSO-de�nable tree-to-tree transductions are character-

ized by macro tree transducers of which the size of the output tree is linear in

the size of the input tree. Moreover, it is shown that it is decidable whether

a macro tree transduction is MSO-de�nable.

Tree transducers are useful as a tool for the transformation of hierar-

chically decomposable graphs. The properties of graph transformations can

then be studied by looking at the properties of the tree transducers used. In

[Dre99,Dre01a] the complexitiy of deciding whether a top-down or bottom-up

tree transducer yields exponentially large output trees is studied. It turns

out to be LOGSPACE-complete for total top-down tree transducers, but

DEXPTIME-complete in general, and P-complete in the bottom-up case.

2.7 2-Structures

Dynamic labeled 2-structures form a network-oriented model of concurrency

and distribution. They also play an important role in graph theory where they

are known as switching classes of gain graphs. One of the central problems is

to determine whether global states with certain properties can occur during

the evolution of the system. This problem has been investigated in terms of

patterns and con�gurations. A number of results concerning the relationship

between patterns and con�gurations have been obtained. A complete intro-

duction to the theory of 2-structures has been published in the book [EHR97].

Results on sizes of switching classes are given in [HH00]. The complexity of

several decision problems concerning gain graphs, and their relationship with

the analogous problems for ordinary graphs was investigated in [EHHR00a].

The investigation of the membership problem for gain graphs, i.e., the question

whether two gain graphs belong to the same switching class, is addressed in

[Hag99], while [EHHR00b] is mainly concerned with pancyclicity, and [HH98]

studies the acyclicity of switching classes. Work is in progress on some purely

combinatorial problems, using forbidden subgraphs; �rst results appear in

[HH01]. All these results, together with some additional material, can be

found in the Ph.D. Thesis of J. Hage [Hag01].

2.8 Deterministic Push-Down Automata

[S�en98b] completely solves the so-called "equivalence problem for Determinis-

tic Push-Down Automata (dpda's)" (which has been open for over 30 years).

This problem can be reformulated as follows: given two equational rooted, de-

terministic graphs G1; G2, is it possible to decide whether they are bisimilar?

This decidability proof can be seen as a veri�cation technique for processes

whose behavior can be described by an equational graph.

[S�en97], [S�en98a] extend the above work to the non-deterministic case,

while [S�en98c] extends it to dpda's with outputs in an abelian group (equiv-

10

Corradini

alently, to graphs with labels belonging to an abelian group). The paper

[S�en99] extends the results of [S�en98a] about the decidability of bisimilarity

for equational rooted, deterministic graphs to the case where the outputs are

taken in any group of matrices over the �eld of rational numbers.

2.9 Programming constructs for graph transformation based languages

In [HP01] a set of programming constructs are identi�ed which ensure that

a programming language based on graph transformation is computationally

complete. These constructs are (1) nondeterministic application of a set of

graph transformation rules, (2) sequential composition, and (3) iteration. This

language is minimal in that omitting either sequential composition or iteration

results in a computationally incomplete language. By computational com-

pleteness we refer to the ability to compute every computable partial function

on labelled graphs.

2.10 Graph-Theoretical results

Finally, we mention a couple of contributions to Graph Theory. The Ph.D.

thesis [Pel97] provides a detailed structure of the automorphism groups of var-

ious kinds of in�nite graphs, in order of complexity: context-free, equational

and automatic. In [BE97c] a new notion of treewidth is studied, closely related

with apex graph grammars.

3 Speci�cation

3.1 Speci�cation of Open and Reactive Systems with Graph Transitions and

Views

Reactive systems perform their tasks through interaction with their users or

with other systems (as parts of bigger systems). An essential requirement

for modeling such systems is the ability to express this kind of interaction.

Classical rule-based approaches like Petri nets and graph transformation are

not suited for this purpose, because they assume to have complete control over

the state of the systems and its transformation.

In order to improve the expressive power of graph transformation systems

for the modeling of open, reactive systems, graph transitions were introduced

in [HEWC01]. A graph transition based on a given graph production is a

rewriting step where not only the e�ects prescribed by the production are

performed (that is, the deletion, preservation and creation of speci�c graph

items), but also additional changes may be performed, namely the addition or

deletion of other items, as if these were caused by the environment. Conceptu-

ally, there is no implicit frame condition for this kind of graph manipulation:

graph productions are considered as incomplete descriptions of the transfor-

mations to be performed. Technically speaking, graph transitions are de�ned

11

Corradini

using a double-pullback construction, in contrast to classical graph derivations

based on a double pushout. The above paper presents two characterization re-

sults which relate graph transitions to the classical double-pushout derivations

and to amalgamated derivations, respectively. Moreover, a loose semantics for

graph transformation systems is de�ned, which associates with each system

a category of models (deterministic transition systems) de�ned as coalgebras

over a suitable functor. Such category has a �nal object, which includes all

�nite and in�nite transition sequences.

Building on these results, the aim of [HEWC97] is to enrich the expres-

sive power of this modelling formalisms by introducing constraints for graph

transformation, in order to restrict the loose semantics of graph transformation

systems mentioned above. The coalgebraic framework makes it possible to de-

�ne a general notion of logic of behavioural constraints. Instances include, for

example, start graphs, application and consistency conditions, and temporal

logic constraints. It is shown that the considered semantics can be restricted

to a �nal coalgebra semantics for systems with behavioural constraints.

In [EHL+00] several constructions for graph transitions are presented, such

as the necessary and suÆcient conditions for the existence of graph transitions,

minimal double-pushout transitions, and results concerning the independence

of transitions, local Church-Rosser properties and parallelism. Furthermore,

the conceptual framework is applied to Petri nets as well, leading to the no-

tion of open step. The approach is further generalized in [ERP98], where a

framework is presented for extending graph transitions and other rule-based

formalisms in such a way that transformations with incomplete information

can be handled. This extension is motivated by the need to model the behav-

ior of open systems in di�erent application areas using graph transformations

and Petri nets. The problems are also discussed for DNA-computing and other

rule-based formalisms.

The idea of a combined reference model- and view-based speci�cation ap-

proach has been proposed recently in the software engineering community. In

[EHTE97] and [EEHT97], a speci�cation technique based on graph transfor-

mations is presented which supports such a development approach. The use of

graphs and graph transformations supports an intuitive understanding and an

integration of static and dynamic aspects on a well-de�ned semantical base.

On this background, formal notions of view and view relation are developed

and the behavior of views is described by a loose semantics. A construction

for automatic view integration is de�ned which assumes that the dependencies

between di�erent views are described by a reference model. The views and

the reference model are kept consistent manually, which is the task of a model

manager. All concepts and results are illustrated with an example of a bank-

ing system. The overall approach if surveyed in [HEET99]. Furthermore, it is

exploited in [Hec98a] for the compositional veri�cation of speci�cations. The

idea is that a view provides an incomplete speci�cation describing only a cer-

tain aspect of the overall system. A view anticipates the (potential) behavior

12

Corradini

of the complete system by its loose semantics. This ensures that properties

of the view are inherited by the complete system. By exploiting this fact,

one may verify temporal properties by decomposing a speci�cation into sev-

eral views, analyzing them separately, and deriving the desired property from

properties shown for the views.

The thesis of Reiko Heckel [Hec98b] brings the concepts just reviewed

(graph transitions and views) into a consistent, unifying conceptual framework

designed for the compositional modelling of concurrent and reactive systems,

based on Open Graph Transformation Systems. To verify temporal properties,

a large speci�cation is decomposed into several views, which are analyzed

separately. Then the properties of the original speci�cation are derived from

the properties of the views. Furthermore, a functorial semantics for open

graph transformation systems is developed based on their loose semantics.

This semantics is taken as a basis for the correctness of the compositional

veri�cation of temporal properties of the systems.

In [BCEH01] in order to model the behaviour of open reactive systems

by means of Petri nets, open Petri nets are introduced as a generalization

of the ordinary model where some places, designated as open, represent the

interface of the reactive system towards the environment. As a consequence of

the interaction with the environment, tokens can freely appear and disappear

in the open places of a net. Open nets are endowed with a truly concurrent

semantics based on open processes, which are an extension of the Goltz-Reisig

(deterministic) processes.

3.2 Modelling of Open Systems using Tiles

When considering abstract equivalences as, e.g., bisimilarity, a key point to

compositionality is the congruence property, which guarantees that equivalent

components can safely replace each other in any system. The de�nition of SOS

formats ensuring that bisimilarity on closed terms is a congruence has received

much attention in the last two decades. For dealing with open terms, the con-

gruence is usually lifted from closed terms by instantiating the free variables in

all possible ways. Papers [BdMM00a,BdMM00b] present an approach based

on tile logic (tl) [GM00], where closed and open terms are managed uniformly,

and study the congruence property for several tile formats, accomplishing dif-

ferent concepts of open systems, where, e.g., con�gurations are de�ned by

term-graphs instead of ordinary terms. In fact, tiles are rewrite rules with side-

e�ects handling very general notion of con�gurations and observations, which

are just required to have suitable sequential and parallel compositions. The

categorical foundations of several tile formats whose con�gurations and ob-

servations have analogous additional structure (e.g. symmetries, cartesianity)

have been investigated in [Bru99,BMM98c,BMM01], in terms of the original

notion of symmetric monoidal and cartesian double categories.

When con�gurations and observations come equipped with the same basic

13

Corradini

algebraic operations, tile logic is also suitable for modeling open ended sys-

tems, where dynamic recon�guration is obtained by observing suitable con-

text embeddings. In particular, the approach can be stretched to deal with

structural axioms on con�gurations, still guaranteeing the important property

that `bisimilarity is a congruence' [BMS00]. In the full version of the paper

([BMS01]) the approach is applied to the case study of the �-calculus, show-

ing that open bisimilarity and tile bisimilarity coincide. The duality between

context and instantiation closure, which is evident in the categorical models

of tiles, is well exempli�ed by the application to logic programming [BMR01],

where a freely generated double category of pullbacks is employed to model

uni�cation.

The simplest class of tiles, where both con�gurations and observations are

multisets of basic elements, has been shown to provide Petri nets with the

notion of concurrent transaction. The resulting tile models are called zero-

safe nets and have been investigated in [BM97,BM98c,BM00b], together with

the application to several case studies. In [BM00a] a distributed interpreter

for zero-safe nets is de�ned, which is reminiscent of the ordinary net unfolding,

while in [BM01a] the approach has been extended to deal with read arcs (which

allow for multiple access in reading to the same token). An application of zero-

safe nets with read arcs to the concurrent modeling of Linda with transactions

is presented in [BM01b]. A tutorial introduction to zero-safe nets is given

in [BM99b].

The introduction of higher order versions of tl for an automatic treatment

of name passing and name creation in mobile calculi is considered in [BM99a],

with application to the �-calculus. Correspondingly, categorical models of

higher order tl have been de�ned by means of the original notion of cartesian

closed double category.

Though at present no automated veri�cation tool is available which is

based directly on tl, some prototyping has been made possible for suitable tl

speci�cation classes, via a conservative encoding in rewriting logic, as reported

in [BMM98c,BMM98b,BMM99,BMM98a]. In particular, the implementation

of tl exploits re ection in rewriting logic to de�ne suitable internal strategies

for controlling rewrites and is written in the language Maude [CDE+99].

3.3 Speci�cation of graph properties by Monadic Second Order Logic

Basic properties of the equational and recognizable subsets of general alge-

bras are reviewed in [Cou96a]; these sets can be seen as generalizations of the

context-free and regular languages respectively. This approach, based on Uni-

versal Algebra, facilitates the development of the theory of formal languages

so as to include the description of sets of �nite trees, �nite graphs, �nite hy-

pergraphs, tuples of words, partially commutative words (also called traces)

and other similar �nite objects.

Descriptive complexity is concerned with the characterization of complex-

14

Corradini

ity classes by logical formulas. Of special interest are formulas of Monadic

Second Order Logic (MSOL) starting with existential set quanti�cations, and

followed by �rst order quanti�cations. In [Cou97b] the main basic graph

properties are reviewed in the perspective of expression by these formulas. In

particular, it considers constructive expression of planarity where the formula

describes a planar embedding. This should be contrasted with the classical

negative characterization by Kuratowski's theorem, which says nothing of the

planar embedding of a graph recognized as planar.

In [Cou96b] some answers are given to the following general question: for

which classes of graphs C is it possible to specify a linear ordering of the set of

vertices of each graph of C by a �xed monadic second-order formula? It is also

investigated whether recognizability and monadic second-order de�nability are

the same for subclasses of C, and whether the hierarchical algebraic structure

of a graph from C can be de�ned in (an extension of) monadic second-order

logic.

In [BE97b,BE97a] it is shown that monadic second order logical proper-

ties of the nodes of trees can be implemented by attribute grammars with

boolean values only, whereas MSO relations between the nodes of trees can be

implemented by tree-walking automata with MSO tests. These characteriza-

tions can be used to implement MSO de�nable tree transductions by attribute

grammars, as shown in [BE00].

It is known that a language is context-free i� it is the set of borders of the

trees of a recognizable set, where the border of a (labelled) tree is the word

consisting of its leaf labels read from left to right. In [CL98] a generalization

of this result in terms of planar graphs of bounded tree-width is given. Here,

the border of a planar graph is the word of edge labels of a path which borders

a face for some planar embedding. It is shown that a language is context-free

i� it is the set of borders of the graphs of a set of (labelled) planar graphs of

bounded tree-width which is de�nable by a formula of monadic second-order

logic. In [Lap98] it is shown that for each k, there exists a monadic second-

order transduction that associates with every graph of tree-width at most k

one of its tree-decompositions of width at most k. Together with a known

result by Courcelle it follows that every set of graphs of bounded tree-width

is CMSO-de�nable if and only if it is recognizable.

Certain graphs, such as cographs, have a unique hierarchical decompo-

sition. It is natural to ask whether this decomposition can be de�ned (in

a precise sense) by means of formulas of monadic second-order logic. For

cographs this is possible, provided the graph is given with an auxiliary linear

order. In [Cou99], the unique decomposition of connected graphs as de�ned

by Tutte is investigated in this perspective and it is proved that it is de�nable

by MSO formulas.

The papers [Cou00b,Cou00c] consider the formalization with relational

structures of graph drawings, with or without edge crossings, where properties

of drawings are formalized with monadic second order logic. By Kuratowski's

15

Corradini

Theorem, nonplanar graphs can be characterized by an existential MSO for-

mula. When the considered graph is planar, the non-validity of this formula

gives no information on its planar drawings: it is of interest to de�ne by MSO

formulas the combinatorial map (a �nite logical structure) underlying a possi-

ble drawing. It is proved in [Cou00b] that a planar map of a linearly ordered

planar graph is MSO de�nable.

There are two ways to express graph properties in monadic second order

logic: with and without edge set quanti�cations. Improving previous results it

is proved in [Cou01c] that edge set quanti�cations can be removed for graphs

having a number of edges linearly bounded in terms of the number of vertices.

Hierarchical decompositions of graphs are studied in [CMR99,CMR00,CO00].

They are important for eÆcient graph algorithms, and they underly graph gen-

eration by grammars, making an algebraic formalization of these grammars

possible. In particular, graph decompositions related to clique-width yield lin-

ear algorithms for problems formulated in monadic second-order logic without

edge quanti�cations. The construction of polynomial graph algorithms based

on the logical descriptions of problems in MSO logic is further studied on

[CMR01], while the study and comparison of di�erent types of graph struc-

turing, in terms of graph operations is addressed in [Cou01b,CM01].

The use of pebbles by tree-walking automata is investigated in [EHvB99,EH99].

It is shown in [EHvB99] that trips on trees are de�nable in monadic second-

order logic i� they can be executed by tree-walking marble/pebble automata.

In [EH99] it is shown that all �rst-order de�nable tree languages can be recog-

nized by tree-walking automata with pebbles that have nested lifetimes, and

that such automata recognize regular tree languages only.

Monadic second order logic on the binary tree (S2S) is very powerful and

subsumes various logics used in concurrency such as branching time temporal

logic or the mu-calculus. It is shown in [JL99] that S2S does not collapse to

its level �2, and does not even collapse to boolean combinations of �2. An

example for the �rst assertion is the S2S formula saying that, for some �xed

subset S of the binary tree, there is a path which meets S in�nitely often.

Papers [Cou00a,Cou01a] are surveys of some research topics discussed in

this subsection.

3.4 Modal and Temporal Logics for Graph Transformation

In [GHK00] graph-interpreted temporal logic is introduced as a speci�cation

logic to be used in conjunction with rule-based speci�cations based on graph

transformation. It specializes propositional temporal logic by interpretating

formulas on transition systems where the states are graphs, i.e., graph transi-

tion systems. It is shown that graph transition systems have the same discrim-

inating power as general transition systems. Thus any sound and complete

deduction calculus for propositional temporal logic is also sound and complete

for the graph-interpreted variant. Properties of the states are expressed by

16

Corradini

graphical constraints which interpret the propositional variables in the tempo-

ral formulas. For any interpretation a graph transition system is constructed

which is typical and fully abstract. Typical here means that the constructed

system satis�es a temporal formula if and only if the formula is true for all

transition systems with this interpretation. By fully abstract it is meant that

any two states of the system that cannot be distinguished by graphical con-

straints are equal. Thus, for a �nite set of constraints we end up with a �nite

transition system which is suitable for model checking.

In the thesis of Manuel Koch ([Koc99]), graph-interpreted temporal logic

has been generalized to distributed graph transformation. Similarly to [Hec98b],

the reasoning from the local satisfaction of local formulas in a subsystem of

a distributed system to global satisfaction of global formulas in the complete

distributed system is supported.

3.5 Integration of Data and Behavioural Speci�cation Formalisms

In [EO01], a general classi�cation of data type and process speci�cation tech-

niques is presented. Moreover, an integration paradigm for system speci�-

cation is proposed which provides a uniform approach on a conceptual level.

The key idea is to consider four di�erent layers which correspond to di�erent

kinds of integrated views of system speci�cation. The formal model for the

four layers, called data type, data states and transformations, processes and

system architecture layers respectively, is based on an integration of abstract

data types and structured transition systems. This formal model can be in-

stantiated by all kinds of basic and integrated modeling techniques. A large

variety of data type and process-driven speci�cation approaches, including Al-

gebraic high-level nets, attributed graph transformation, an integration of Z

with statecharts, and some diagram techniques of UML, are brie y discussed

as instances of the integration paradigm.

In [EPO01], Ehrig, Padberg and Orejas distinguish between basic spec-

i�cation formalisms concerning mainly one view or aspect of a system, and

integrated formalisms taking care of di�erent views and aspects. Basic views

are considered as the data type and process view and time constraints as an

important additional aspect. An overview of corresponding basic speci�cation

formalisms is given and furthermore, discussed how they can be combined or

integrated in order to handle combination and integration of di�erent views

and aspects.

3.6 Other approaches: Coupled Graph Grammars and Graphical SOS.

In [Gru00a], a speci�cation method for distributed data modeling based on

coupled graph grammars is presented. This method is able to uniformly de-

scribe legal domain con�gurations used in distributed modeling as well as

re-engineering tasks. The speci�cation method supports the development of

proper (re)design tools, and the method is tool-supported itself.

17

Corradini

The Structured Operational Semantics (SOS) is a popular and powerful

style of language speci�cation providing a rich mathematical theory and a

well-established methodology. In visual modeling techniques like the UML, the

abstract syntax is speci�ed by a meta model, i.e., a class diagram or schema

describing the static structure of the models. A concrete model, typically

given by a set of interrelated diagrams of various kinds, is represented as

an abstract syntax graph conforming to this schema. In order to specify

the operational semantics of a diagrammatic language (i.e., a dynamic meta

model), in [CHM00] the SOS methodology is applied to the graphical abstract

syntax. The idea is to replace SOS program terms with abstract syntax graphs,

augmented with a representation of the state, and to use graph transformation

techniques for specifying an operational semantics.

4 Structuring aspects

4.1 Distributed Graph Transformation

The new approach to distributed graphs and graph transformation (DGT) as

presented in [Tae96] allows to use structured graph transformation on two ab-

straction levels, the network and the local level. The network level contains the

description of the topological structure of a system. The local level concerns

the description of states and their transitions in local systems. Local state

transitions may depend on others using suitable synchronization mechanisms.

The main distribution concepts of categorical graph grammars proposed by

Schneider are combined with the algebraic double-pushout approach to dis-

tributed graph transformation introduced by Ehrig et.al. The theory of Dis-

tributed Graph Transformation is extended to attributed graphs in [TK97],

using partial algebras for the description of data and data operations, and

leading to a powerful and exible attribution mechanism of graph transforma-

tion. The approach is further extended in [Tae99] by considering splitting and

joining of local graphs, as well as parallel transformations in local systems.

Distributed systems demand a number of requirements on speci�cation

techniques which do not have to be taken into account for the development

of non-distributed software. In [FKTV99], new concepts for visual design

of distributed systems are presented which are based on DGT as underlying

formal speci�cation technique. The kernel of this technique focuses on a struc-

tured graph with two abstraction levels, the network and the local level, and

its transformation. On the network level, the (possibly) dynamic topological

structure of the system is speci�ed. The local level contains the graphical

description of local object and data structures where parts of them may be

replicated in remote network nodes. Those structures may evolve indepen-

dently or synchronized with remote structures, using a interaction mechanism

based on subactions. The approach is illustrated with a reference application

modeling a distributed version management system for any kind of document.

18

Corradini

To support the design of distributed systems by several developers, local

views are introduced in [FKTV99,FKT00]. A local view on a distributed

system consists of one local system, its import and export interfaces, and

connected remote interfaces. The behavior of a local system is speci�ed by a

set of graph rules that are applicable only to the local view of the system. Local

systems communicate either synchronously or asynchronously via their import

and export interfaces. Asynchronous communication is modeled by sequential

application of graph rules, synchronous communication by the amalgamation

of graph rules.

Distributed algorithms and dynamic distributed data structures are basic

aspects of distributed systems which usually are modelled separately by dif-

ferent speci�cation techniques. In the running example of the mutual access

to �le systems, typical problems are shown in [TE00] which cannot be handled

by separate modelling. The paper discusses how these problems can be solved

by the integrated speci�cation of distributed algorithms and dynamic data

structures by distributed graph transformation.

In [TGM99,GMT99,TGM00,GEMT00a,GEMT00b] several di�erent appli-

cations of Distributed Graph Transformation to dynamic architecture con�g-

uration for distributed systems and viewpoint-oriented software development

have been developed. The problem of specifying dynamic change in distributed

systems is addressed in [TGM99] and [TGM00]. Change in distributed sys-

tems is related to at least two levels. One is the management of change in local

nodes of the distributed system and how such a change is then propagated to

those nodes which need to know about the change. The other aspect is chang-

ing the structure of the distributed system itself. This implies e.g. to add

and/or remove a local node or an entire subsystem to/from the distributed

system. In [TGM00] it is discussed how distributed graph transformation is

used to realize the change model. An example - a ring database - shows how

DTS can be used to model these changes in a small but non-trivial distributed

system.

In order to support multiple perspectives in software development one

needs a scheme which expresses explicitly all the views held by the various

stake-holders like requirement engineers, software architects, clients, users,

etc. The ViewPoint framework has been developed in the past as a con-

ceptual model for expressing such a multiple perspective steeing in software

development projects. In [GEMT00a], this framework is formally described by

DGT, and the applicability of this approach is demonstrated with a non-trivial

sample system. In [GEMT00b], the ViewPoint Tool is presented which sup-

ports the de�nition and usage of multiple views based on the above mentioned

approach.

A visual modeling technique for distributed object systems based on graph

transformation is presented in [Tae02]. It includes the graphical description

of the network and its dynamic recon�guration as well as the component

interfaces and local object systems and their behavior. Typical issues in dis-

19

Corradini

tributed systems like remote object interaction, object migration and repli-

cation, communication and synchronization are expressible in this technique.

The notation is close to UML, extending it where needed.

A related approach is presented in [MR99], and it is based on the fact

that graphs and graph grammars can be fruitfully used to model distributed

systems which behave in a synchronized way. In fact, graphs can represent

networks of processes, and suitable graph rewriting rules, based on the combi-

nation of simple context-free productions via a synchronization mechanisms,

can represent the dynamics of such systems. To cope with the problem of

eÆciently combining productions together, the paper proposes to use well-

known constraint propagation techniques, which can help reducing the possi-

ble choices for each process and thus simplify the combination problem.

In [Koc97], distributed graph transformation is extended to allow applica-

tion conditions for distributed rules. This extended formalism is applied to

model a distributed database transaction model. The thesis of Manuel Koch

([Koc99]) propeses speci�cation techniques based on temporal logics for a

variant of Distributed Graph Transformation based on the single-pushout ap-

proach. The approach permits a variety of speci�cation techniques to describe

the local data and object structures, and provides a compositional operational

semantics. Such a semantics is based on algebra transformation systems, as

presented in [Gro98]. To support not only the modeling and speci�cation of

distributed systems, but also their veri�cation, DGT has been integrated with

temporal logic. Local formulas holding in subsystems can directly be used

to reason about the satisfaction of global formulas for the whole distributed

system.

4.2 Software Architecture

The description of a software architecture style must include the structural

model of the components and their interactions, the laws governing the dy-

namic changes in the architecture, and the communication pattern. In [HIM98,HIM99]

a system is represented as a graph where hyperedges are components and

nodes are communication ports of communication. The construction and dy-

namic evolution of the style is represented as context-free productions and

graph rewriting. To model the evolution of the system it is proposed to use

techniques of constraint solving. From this approach one obtains not only an

intuitive way to model systems with nice characteristics for the description

of dynamic architectures and recon�guration, but also a unique language to

describe the style, model the evolution of the system, and prove properties.

The paper [HM99] presents a method for specifying recon�gurations or

transformations over software architectures, being sure that if the transforma-

tion can be speci�ed, then its application over the system will be consistent

with respect to the architecture style. Styles are described by context-free

hyperedge graph grammars. In this context, a software architecture is de-

20

Corradini

termined by a graph generated by the grammar. The formalization of the

method is introduced in two ways. The �rst approach is a visual presentation

and has the intention of showing that it can be used by software architects in

real life in a simple way. The second approach presents a formal model for the

�rst one using second-order lambda-terms and tile sequents, and shows that

the appoach is easily implementable.

The recon�guration mechanism of software architectures is extended in

[HIM00] by allowing the declaration, creation and matching of new nodes (i.e.

ports of communication) and using constraint solving over the productions of

the style grammar for achieving synchronization. In this way complex evo-

lutions can be speci�ed in a more expressive and compact form than using

�-calculus style languages for mobility. A similar approach is proposed in

[HM00], where graphs, productions and derivations are characterized as cer-

tain terms of a simply typed �-calculus, and hyperedge replacement can be

eÆciently implemented as �-conversion.

Papers [HM01a,HM01b] introduce a graphical model for the design of soft-

ware systems that include mobility or dynamic recon�guration of their compo-

nents based on Synchronized Hyperedge Replacement Systems with the addi-

tion of name mobility. The capability of creation and sharing of ports together

with multiple simultaneous synchronizations provides a very powerful tool to

specify more complex evolutions, recon�guring multiples components by iden-

tifying speci�c ports. This method gives a solid foundation for graphical

mobile calculus which are well-suited for high level description of distributed

and concurrent systems.

4.3 Hierarchical Graphs

If systems are speci�ed by graph transformation, large graphs should be struc-

tured in order to be comprehensible. The paper [DHP01] presents an approach

to the rule-based transformation of hierarchically structured (hyper)graphs

where distinguished hyperedges contain graphs that can be hierarchical again.

This framework extends the well-known double-pushout approach from at

to hierarchical graphs. The paper shows how pushouts and pushout comple-

ments of hierarchical graphs can be constructed recursively. Moreover, rules

are made more expressive by introducing variables which allow to copy and

to remove hierarchical subgraphs in a single rule application.

In [BKK01] a new hierarchical graph model is introduced which allows

to structure large graphs into small components by distributing the nodes

(and edges likewise) into a hierarchy of packages. In contrast to other known

approaches, the type of underlying graphs is not �xed. The model is equipped

with a rule-based transformation concept such that hierarchical graphs cannot

only be used for static representation of complex system states, but also for the

description of the dynamic system behaviour. In [BH01], existing approaches

to hierarchical graphs are simulated in this model, allowing one to compare

21

Corradini

their features and expressive powers.

4.4 Modularity Concepts: GRACE and Transformation Units

grace is a graph transformation language for specifying and programming

graph-centered environments that is being developed by researchers from Aachen,

Berlin, Bremen, Erlangen, Hildesheim, M�unchen, and Paderborn.

The basic concept of grace is the transformation unit [KK99b] which

allows for systematic and structured speci�cation and programming based on

graph transformation, and this independently of a particular graph transfor-

mation approach. A transformation unit comprises a set of rules, descriptions

of initial and terminal graphs, and a control condition. Moreover, it may im-

port other transformation units for structuring purposes. A transformation

unit transforms initial graphs to terminal ones by interleaving rule applica-

tions with calls to imported units. Thus, each transformation unit de�nes a

graph transformation, i.e. its semantics is a binary relation between initial and

terminal graphs which is given by interleaving sequences.

In [KKS97] called nested graph transformation units are introduced. A

system can be modelled by a (possibly cyclic) network of local graph transfor-

mation units that re ects the import structure of the system. It is shown that

nested graph transformation units have a reasonable operational semantics,

which is obtained by iterating the so-called interleaving operator.

A thorough study of the theory of transformation units is presented in

Sabine Kuske's thesis [Kus00]. Transformation units can be clustered into

transformation modules [DKKK00,HHKK00]. A module may have an im-

port interface consisting of formal parameter units and an export interface

consisting of the units that are made available to the environment. The for-

mal parameter units can be instantiated by exported units of other modules

so that large classes of similar transformation units can be described in a

manageable and �nite way. This allows to specify operations on graphs in a

loose way and may be instantiated by exported transformation units of other

modules through module composition. In [Kus02] the components of a param-

eterized transformation unit are typed expressions containing typed variables

as parameters. It turns out that parameter instantiation of a parameterized

transformation unit yields again a parameterized transformation unit and is

associative.

In [KK00c] transformation units and transformation modules are gener-

alized in such a way that they can be used for the structuring of arbitrary

rule-based systems. In [KK00b] the units and the modules of a system may

be based on di�erent semantic domains and di�erent types of rules and rule

applications as long as the formats of the con�gurations are compatible with

each other. In this sense, the proposed approach supports the design of mod-

ular systems with heterogeneous components.

In [Kus01] it is shown how transformation units can be used to formalize

22

Corradini

the execution semantics of UML state machines. In more detail, a UML state

machine is described as a structured graph transformation system in such a

way that the wellformedness rules of UML state machines are satis�ed and

the �ring of a maximum set of enabled non-con icting transitions corresponds

to the application of a graph transformation rule.

In [tHBG99] the concept of an instance level module is introduced to en-

capsulate objects in an object-oriented model. This concept is based on pack-

ages from the industry standard UML. This paper sees the general issue of

structuring graphs from the perspective of object orientation.

4.5 Modules for Typed Graph Transformation Systems and Re�nement Re-

lations

A module is basically given by export and import interfaces, and a body that

implements the features o�ered by the export interface in terms of the features

required in the import interface. In [GPS97,GPS98] two kinds of re�nement

relations between GTS are investigated. In a spatial re�nement each rule

is re�ned by an amalgamation of rules while in a temporal re�nement it is

re�ned by a sequence of rules: in both cases, the re�nement relation supports

the modeling of implementation. Pushouts of re�nements are shown to exist,

thus allowing the de�nition of operations on modules, such as composition,

with a predictable compositional semantics.

In [GSP99,GPS00,GPS01] the properties of spatial and temporal re�ne-

ments are further investigated. Furthermore, they are employed for the de-

velopment of a module concept for Typed Graph Transformation Systems

(TGTS). In [GPS00], graph transformation systems are considered as formal

models of computational systems, speci�ed by rules which describe the atomic

steps of a system. A re�nement of a graph transformation system is given by

associating with each of its rules a composition of rules of a re�ning system,

that has the same visible e�ect as the original rule. The basic composition op-

erations on graph transformation rules are sequential and parallel composition,

corresponding to temporal and spatial re�nement respectively. Syntactically,

re�nements are represented by rule expressions that describe how the re�ning

rules shall be composed.

For the development of larger systems, it is important that a modeling

technique o�ers a stringent module concept. Each module has to support the

encapsulation of data structure as well as functionality also at runtime. Mod-

ular graph transformation, presented in [GPST00] and based on the module

concept proposed in [GPS98], supports these features. Modules are built up

of speci�cations where attributed graphs describe the static data structures,

whereas the dynamic behavior is modeled by the controlled application of

graph rules. Rule expressions are used to formulate the control ow.

In [GPS01] the previous work is integrated to provide a comprehensive

study of re�nements and modules for typed graph transformation systems to

23

Corradini

support the software speci�cation development in both dimensions: modules

for the horizontal structuring of a speci�cation, i.e., its composition from feasi-

ble parts, and re�nements for the development over time. Re�nement is shown

to preserve the behaviour, modules can be combined using their interfaces, and

subtype re�nement can be simulated using the typing mechanism.

An abstract categorical theory on modularization of graph transformation

systems has been developed in the thesis of Marta Simeoni ([Sim00]); it is for-

malized independently of any particular approach on graph transformation.

The instantiation of the abstract theory over a concrete approach follows au-

tomatically by providing formal proofs to the generic categorical requirements

pointed out within the abstract theory. In particular an instantiation for the

Local Action Systems approach has been demonstrated.

4.6 Colimit constructions

For the treatment of structuring mechanisms categorical constructions based

on colimits are often used in Computer Science. Application areas include

the structuring and re�nement of formal speci�cations based on colimits in

the category of signatures, operational semantics of functional logic program-

ming languages based on the category of jungles, and Algebraic Development

Techniques and their extensions (e.g. Statecharts, Graph Grammars, Alge-

braic High-Level Petri Nets, Action Nets or Dynamic Abstract Data Types).

These applications can be based on the computation of colimit in two cate-

gories, namely signatures and graph signatures. In [Wol98], a new constructive

proof of cocompleteness for sets, signatures and graph structures with partial

morphisms is given. This proof establishes an (almost) linear complexity of

the colimit constructions in all these categories. Moreover, a library for col-

imit computations in these categories implemented in Ei�el, Java and C++

is provided. The algorithms are directly derived from the constructed proofs

mentioned above. The application of the colimit library in di�erent areas both

in the context of speci�cation languages and graph transformation is outlined.

5 Semantics

5.1 Concurrent Semantics of Algebraic Graph Grammars

The broad objective of this research thread within GETGRATS has been to

consolidate the foundations of the concurrency theory for dpo graph transfor-

mation systems, by extending to this more general setting some fundamental

approaches typical of Petri net theory.

The chapter [BCE+99] reviews and compares various concurrent semantics

for the double pushout (DPO) algebraic approach to graph transformation, us-

ing di�erent mathematical structures and describing computations at di�erent

levels of abstraction. A trace semantics is �rst discussed, based on the clas-

sical shift equivalence on graph derivations. Next the notion of graph process

24

Corradini

is presented, which lifts to the graph transformation framework the notion of

non-sequential process for Petri nets. Trace and process semantics are shown

to be equivalent, in the sense that given a graph transformation system, the

corresponding category of derivation traces and that of (concatenable) pro-

cesses turn out to be isomorphic. Finally, a more abstract description of

graph transformation systems computations is given by de�ning a semantics

based on Winskel's event structures.

The papers [BCM98,BCM99] face the problem of de�ning an unfolding

semantics for graph transformation systems in the double-pushout approach,

generalizingWinskel's seminal work on the semantics of Petri nets. In [BCM98]

it is suggested how a graph grammar can be unfolded into an acyclic branch-

ing structure, that is itself a (nondeterministic occurrence) graph grammar

describing all the possible computations of the original grammar. The cor-

respondence with Winskel's work is pushed further in [BCM99], where it is

shown that the unfolding can be abstracted naturally to a prime algebraic

domain and then to an event structure semantics. Such event structure co-

incides both with the one de�ned by Corradini et al. via a comma category

construction on the category of concatenable derivation traces (also reviewed

in the above mentioned [BCE+99]), and with the one introduced by Schied,

based on a deterministic variant of the DPO approach.

The mentioned results have been collected and extended in the thesis of

Paolo Baldan ([Bal00], see also [Bal02]). Here the construction which asso-

ciates to each graph grammar its nondeterministic unfolding, an (appropriate

kind of) event structure and �nally a domain, is developed at categorical level

as a chain of functors. More precisely, all the steps but the second one are

characterized as categorical core ections (see also [BCM00c]). The process

semantics for graph grammars, which was originally developed as an indepen-

dent piece of work, is shown to emerge naturally from the above theory.

The �rst part of the thesis lays the conceptual basis for the treatment of

grammars by developing an analogous theory for two generalizations of Petri

nets in the literature, which reveal a close relationship with graph transforma-

tion systems, namely contextual nets (also called nets with read, activator or

test arcs) and inhibitor nets (or nets with inhibitor arcs). In the treatment of

contextual nets a basic role is played by asymmetric event structures, which

generalize prime event structures by allowing a non-symmetric con ict rela-

tion. The generalization to inhibitor nets, requires the de�nition of a new, very

general, notion of event structure, called inhibitor event structure, to faithfully

express the dependency among events arising from the non-monotonicity of

the enabling. Inhibitor event structures turns out to be expressive enough

to model graph grammar computations and the theory developed for graph

grammars can be presented as a lifting of the corresponding theory for in-

hibitor nets. A re�ned version of the work on contextual nets appears also

in [BCM00a], while the unfolding semantics of inhibitor nets has been pre-

sented also in [BBCP00a,BBCP00b].

25

Corradini

The mentioned semantics for graph transformation systems provides a de-

scription of the concurrent behaviour of the system in terms of structures

which are, in general, non e�ective (in�nite, undecidable). However, a con-

crete truly concurrent semantics is intended to represent the basis for the

de�nition of more abstract observational semantics, which takes into account

only some aspects of interest for the system at hand and which can be used

to develop e�ective (possibly approximated) veri�cation techniques.

The paper [BCK01] proposes a veri�cation technique for graph transfor-

mation system which exploits the unfolding semantics. More precisely, the

paper presents an algorithm which, given a graph transformation system and

a start graph, produces a �nite structure consisting of a hypergraph decorated

with transitions (Petri graph) which can be seen as an approximation of the

Winskel's style unfolding of the graph transformation system. The fact that

any reachable graph has an homomorphic image in the Petri graph and the

additional causal information provided by transitions allow us to prove several

interesting properties of the original system. As an application of the proposed

technique it is shown how it can be used to verify the absence of deadlocks in

an in�nite-state Dining Philosophers system.

The paper [BCM00b] proposes an abstract semantics for contextual nets

based on history preserving bisimulation (HP-bisimulation), a behavioural

equivalence which, di�erently from ordinary bisimulation, is sensible to the

concurrency properties of the systems. Resorting to HD-automata, a varia-

tion of ordinary automata suited to deal with history-dependent formalisms,

HP-bisimulation is shown to be decidable for �nite-state contextual nets and

an algorithm is proposed to decide such equivalence. This work has been gen-

eralized to graph transformation systems in [BCM01], where also the logical

counterpart of HP-bisimulation, i.e., a logic in the style of Hennessy-Milner

adequate for HP-bisimulation, is presented.

A notion of bisimulation for graph rewriting systems is introduced in

[KM01], allowing one to prove observational equivalence for dynamically evolv-

ing graphs and networks. The framework of synchronized graph rewriting with

mobility is used, and it is described in two di�erent, but operationally equiv-

alent ways: on graphs de�ned as syntactic judgements and by using tile logic.

One of the main results of the paper says that bisimilarity for synchronized

graph rewriting is a congruence whenever the rewriting rules satisfy the basic

source property. Furthermore, an up-to technique is introduced for simplify-

ing bisimilarity proofs, and it is used in an example to show the equivalence

of a communication network and its speci�cation.

5.2 Local Action Systems: Process semantics and Modelling of Petri Nets

For graph rewriting based on node replacement and embedding, the process

semantics of ESM systems [JM96] was taken as a starting point and general-

ized to other types of graph rewriting systems. In a �rst step, the embedding

26

Corradini

mechanism of ESM systems is generalized, and its action is viewed as the

result of a number of local actions, which are associated to pairs of directly

causally related nodes. The resulting type of GTS, called Local Action Sys-

tems, is introduced in [Jan99]. The process notion developed there has several

interesting properties; on the one hand it allows a powerful notion of compo-

sition enabling one to capture the communication between reactive systems,

and on the other hand the behaviour of a given system can be investigated

through the interaction of its processes with an arbitrary set of processes over

the relevant alphabet, without the need to �x a particular context system.

In [Jan99] it is also demonstrated that the approach can be applied to actor

systems, since Actor Grammars are a special case of it.

In [JV99] a construction is given that associates with each partial obser-

vation of a process an operation on the set of graphs on the nodes of that

process; it is shown that the set of these operations has a nontrivial algebraic

structure. This enables one to build equational proofs of various properties

concerning the composition of processes.

The original notion of LAS is further generalized in [JV00] by adding the

temporal order of local actions as an extra component to the processes. It is

shown that the framework obtained in this way can express the well-known

NLC graph rewriting in spite of the fact that the latter are not con uent, and

hence it contributes to unifying the various approaches to graph rewriting.

It is also clear that the additional expressive power can be used to formalize

temporal properties.

Notions of modularity and re�nement morphisms for Local Action Sys-

tems have been developed in the thesis of Marta Simeoni [Sim00]. A module

consists of a set of productions representing its external behaviour- this set of

productions is exported - and an implementation of that set of productions.

This implementation in turn consists of two sets of productions: on the one

hand, interface productions providing a translation of graphs over the external

alphabet into graphs over an internal alphabet, and on the other hand a body

of productions over the internal alphabet. The relation between the exported

productions and the implementation is based on the constructions of [JM96]

and [Jan99], which allow the extraction of productions from processes. The

module concept allows one to handle both data and control abstraction. The

approach is in the line of the one based on Transformation Units, but it di�ers

from it in that the external e�ect of a unit is described by a set of productions

rather than by a relation over graphs.

In [Jan02] it is shown that a process semantics can be developed for a much

broader class of embedding-based graph rewriting systems than just Local

Action Systems. A general process notion for graph rewriting with embedding

is introduced, where the embedding mechanism is a structure enabling one to

construct the result of a process. Subsequently the sequential and concurrent

composition of processes is considered, and necessary conditions are given for

the embedding mechanism to �t in the framework. It is demonstrated that

27

Corradini

not only Local Action Systems, but also other systems, such as Petri nets, are

special cases. It also turns ot that the new approach to processes is capable of

dealing with nontrivial features of the theory of Petri nets, such as asymmetric

con icts for inhibitor nets.

In [JV01] the relationship between Petri Nets and Local Action Systems

for discrete graphs is explored, and in particular the possibility to choose

di�erent ways to encode the markings of a net. It is shown that one gets

LAS systems with the same sequential behavior as the original net, but with

di�erent concurrent behaviors. It turns out that two particular choices (a node

represents either a token or a place) correspond to well-known classes of Petri

Nets. Also, an application is considered in which the concurrent behavior of a

net changes over time, and it is shown that this situation can be handled using

the encoding presented. Thus, while it is not surprising that Petri Nets can

be modeled by Local Action Systems, there is evidence that the latter o�er

suÆcient exibility to serve as a unifying framework for some of the numerous

variants of Petri Nets.

5.3 Categorical representation of Term Graphs and applications

The paper [CG99a] provides a categorical characterization of term graphs that

parallels the well-known characterization of standard terms as arrows of the

algebraic theory of a given signature. In particular, it is shown there that

term graphs over a signature � are one-to-one with the arrows of the free

gs-monoidal category generated by �. Such a category satis�es all axioms for

Cartesian categories but for the naturality of two transformations, providing

in this way an abstract and clear relationship between terms and term graphs.

It is already known that Term Rewriting Systems can be faithfully de-

scribed by a Cartesian 2-category, where horizontal arrows represent terms,

and cells represent rewriting sequences. A similar 2-categorical presentation

is proposed for acyclic term graph rewriting [CG97], based on the main result

of [CG99a].

In [CG98b,CG99c] the approach presented in [CG97] is extended to a cate-

gorical description of possibly cyclic term graph rewriting. It is shown that this

presentation is equivalent to the well-accepted operational de�nition proposed

by Barendregt et. al., but for the case of circular redexes, for which a di�erent

treatment is proposed, and justi�ed formally. The categorical framework is

based on traced gs-monoidal 2-categories, and it allows to model also automatic

garbage collection and rules for sharing/unsharing and folding/unfolding of

structures. Furthermore, it can be used for de�ning various extensions of

term graph rewriting, and for relating it to other rewriting formalisms.

In [CG98a] the rewriting of rational terms is considered. Rational terms

(i.e., possibly in�nite terms with �nitely many subterms) can be represented

in a �nite way via �-terms, that is, terms over a signature extended with self-

instantiation operators. For example, f! = f(f(f(: : :))) can be represented as

28

Corradini

�x:f(x). Now, if one reduces a �-term t to s via a rewriting rule using standard

notions of the theory of Term Rewriting Systems, how are the rational terms

corresponding to t and to s related? The paper answers to this question

in a satisfactory way, resorting to the de�nition of in�nite parallel rewriting

proposed in [Cor93]. It also provides a simple, algebraic description of �-term

rewriting using a variation of Meseguer's Rewriting Logic formalism. A survey

of the results concerned with the categorical description of term graphs and

other term-like structures, as well as of their rewriting, is presented in [CG02].

The characterization of term graphs as arrows of a gs-monoidal category

presented in [CG99a] has been exploited in various ways. It is used, for ex-

ample, in [MR98] and [MR99], where graph grammars are used for modeling

distributed systems which behave in a synchronized way.

Multi-algebras allow to model nondeterminism in an algebraic framework

by interpreting operators as functions from individual arguments to sets of

possible results. In [CG99b] and its full version [CG01], the authors propose

a functorial presentation of various categories of multi-algebras and partial

algebras, analogous to the classical presentation of algebras over a signature �

as cartesian functors from the algebraic theory over � to Set. They introduce

two di�erent notions of theory over a signature, both having a structure weaker

than cartesian, and they consider functors from them to Rel or Pfn, the

categories of sets and relations or partial functions, respectively. In particular,

the theory used for classifying multialgebras is the gs-monoidal theory of a

signature, which was shown in [CG99a] to represent faithfully term graphs

over the signature. Based on this observation, it is argued that the natural

generalization of usual terms for multi-algebras are term graph, and a term

graph syntax is actually used in [CGK00] for designing an inference calculus

for term-graph equational deduction. The soundness of the calculus is proved,

but its completeness remains an open problem.

Building on term graphs and other algebraic structures for expressing for-

malisms di�erent from the standard tree-like presentation of terms, where

e.g. name sharing, name creation and name hiding can be straightforwardly

modeled, it has been possible to identify a kernel of ingredients for describing

normal form presentations of such formalisms (namely, links, interfaces and

modules), showing that they all form di�erent avors of enriched symmetric

monoidal categories [BGM99,BGM01c].

Relations, multirelations, partial functions, equivalences can be seen as

particular instances of the more general concept of span (over Set). A span

consists of a support (a set) and two legs (two arrows in Set having the support

as source). In [BG01] the gs-monoidal structures of several span categories is

investigated, making the correspondence with other classical categories such

as Rel precise.

29

Corradini

5.4 Inductive de�nition of graph transformation

The dynamic behavior of rule-based systems can be traditionally described

in two orthogonal ways. Either operationally, in the sense that a way of

embedding a rule into a state is devised, stating explicitly how the result

is built: This is the role played by (the application of) a substitution in

term rewriting. Or inductively, showing how to build the class of all possible

reductions from a set of basic ones: For term rewriting, this is the usual

de�nition of the rewrite relation as the minimal closure of the rewrite rules.

As far as graph transformation is concerned, the operational view is by far

more popular, but approches based on an inductive view are proposed in

[GH98,GHL99,CGH99,Hec98b].

In [CGH99], the development of an algebra of graph derivations as a de-

scriptive model of graph transformation systems is discussed. For that pur-

pose, a categorical three level approach for the construction of models of com-

putations based on structured transition systems is used. Categorically the

algebra of graph derivations can then be characterized as a double category

with �nite horizontal colimits. One of the main objectives of this paper is to

show how algebraic techniques can be used for the development of this formal

model, in particular to obtain a clear and well structured theory. Thus it

may be seen as a case study in theory design and its support by algebraic

development techniques. The approach is completely formalized in the thesis

of Reiko Heckel [Hec98b].

In [GH98] �rst an inductive description for graphs as arrows of a freely

generated dgs-monoidal category is provided. Then, 2-categorical techniques

can be applied, already known for term and term graph rewriting [CG97],

recasting in this framework the usual description of graph transformation via

double-pushout. A related approach is presented in [GHL99].

5.5 Coalgebraic Semantics of Structured Transition Systems

In [CGH01], Corradini, GrosseRhode and Heckel relate labeled transition sys-

tems and coalgebras with the motivation of comparing and combining their

complementary contributions to the theory of concurrent systems. The well-

known mismatch between these two notions concerning the morphisms is re-

solved by extending the coalgebraic framework by lax cohomomorphisms. En-

riching both labeled transition systems and coalgebras with algebraic structure

for an algebraic speci�cation, the correspondence is lost again. This motivates

the introduction of lax coalgebras, where the coalgebra structure is given by

a lax homomorphism. The resulting category of lax coalgebras and lax co-

homomorphisms for a suitable endofunctor is shown to be isomorphic to the

category of structured transitions systems, where both states and transitions

form algebras. The framework is also presented on a more abstract level us-

ing monads and comonads, extending the bialgebraic approach by Turi and

Plotkin.

30

Corradini

The aim of [CHM99b] is to investigate the relation between two models of

concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules

with side e�ects which are endowed with operations of parallel and sequential

composition and synchronization. Their models can be described as monoidal

double categories. Coalgebras can be considered, in a suitable mathematical

setting, as dual to algebras. They can be used as models of dynamical systems

with hidden states in order to study concepts of observational equivalence and

bisimilarity in a more general setting.

In order to capture in the coalgebraic presentation the algebraic structure

given by the composition operations on tiles, coalgebras have to be endowed

with an algebraic structure as well. This leads to the concept of structured

coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. How-

ever, structured coalgebras are more restrictive than tile models. Those mod-

els which can be presented as structured coalgebras are characterized by the

so-called horizontal decomposition property, which, intuitively, requires that

the behavior is compositional in the sense that all transitions from complex

states can be derived by composing transitions out of component states.

In [CHM99a,CHM01] we address the issue of providing a structured coal-

gebra presentation of transition systems with algebraic structure on states

determined by an equational speci�cation �. More precisely, we aim at rep-

resenting such systems as coalgebras for an endofunctor on the category of

�-algebras. The systems we consider are speci�ed by using arbitrary SOS

rules, which in general do not guarantee that bisimilarity is a congruence. We

�rst show that the structured coalgebra representation works only for systems

where transitions out of complex states can be derived from transitions out of

corresponding component states. This decomposition property of transitions

indeed ensures that bisimilarity is a congruence. For a system not satisfying

this requirement, next we propose a closure construction which adds context

transitions, i.e., transitions that spontaneously embed a state into a bigger

context or vice-versa. The notion of bisimulation for the enriched system

coincides with the notion of dynamic bisimilarity for the original one, that

is, with the coarsest bisimulation which is a congruence. This is suÆcient

to ensure that the structured coalgebra representation works for the systems

obtained as result of the closure construction.

5.6 Algebraic semantics of (contextual) Petri nets

According to the so-called \Petri nets are monoids" approach, the multiset

structure of markings can be lifted to the computation level to characterize

the concurrent net behaviours algebraically. In [BMMS99,BMMS00] we show

that although the algebraic semantics of place/transition Petri nets under the

collective token philosophy can be fully explained in terms of strictly sym-

metric monoidal categories, the analogous construction under the individual

token philosophy is not completely satisfactory, because it lacks universality

31

Corradini

and also functoriality. We introduce the notion of pre-nets to overcome this,

obtaining a fully satisfactory categorical treatment, where the operational se-

mantics of nets yields an adjunction. This allows us to present a uniform

logical description of net behaviors under both the collective and the individ-

ual token philosophies in terms of theories and theory morphisms in partial

membership equational logic [BMMS98,BMMS99]. Moreover, since the uni-

versal property of adjunctions guarantees that colimit constructions on nets

are preserved in our algebraic models, the resulting semantic framework has

good compositional properties [BMMS00].

In [BS00] (full version in [BS01]) the \Petri nets are monoids" approach

is extended to contextual nets by considering monoidal categories of compu-

tations over a non-free monoid of places: a token is regarded as an atom that

can emit several \negative" particles that can be read (but not consumed)

separately.

6 Applications

6.1 Term Graph Rewriting and Term Graph Narrowing

Term Graph Rewriting is concerned with the representation of functional ex-

pressions as graphs, and the evaluation of these expressions by rule-based

graph transformation. Representing expressions as graphs allows one to share

common subexpressions, improving the eÆciency of term rewriting in space

and time.

Computations by term graph rewriting terminate more often than compu-

tations by the corresponding term rewrite systems. For this reason, in [Plu97]

simpli�cation orders on term graphs are introduced and shown to be well-

founded. Thus, these orders can be used in termination proofs. a recursive

path order on term graphs is de�ned by analogy with the well-known order on

terms, and is shown to be a simpli�cation order.

A survey of (acyclic) term graph rewriting is given in [Plu99b], where

emphasis is given to the relations between term and term graph rewriting.

The paper focusses on soundness of term graph rewriting with respect to term

rewriting, on completeness for proving validity of equations and for computing

term normal forms, on termination and con uence, and on term graph narrow-

ing. The �rst part of Plump's habilitation thesis [Plu99a] also surveys term

graph rewriting, while the second part studies termination and con uence|

the key properties for term and term graph rewriting|in the setting of general

graph transformation. A short review of the essentials of term graph rewriting

(concerning soundness, completeness, termination and con uence) is given in

[Plu02].

In [CD97] it is shown that the rewriting of cyclic term graphs (which

denote rational, possibly in�nite terms) is adequate with respect to rational

parallel term rewriting. The approach constrasts with the \classical" one in

32

Corradini

that a single graph reduction corresponds to a single (but possibly in�nite)

parallel term rewrite step whereas, classically, a single graph reduction may

correspond to an in�nite sequence of term rewrite steps.

In [AKP97] a survey of con uence properties of (acyclic) term graph rewrit-

ing is presented. Results and counterexamples are given for plain applications

of rewrite rules, extensions with the operations of collapsing and copying, and

with both operations together. Collapsing and copying together constitute

bisimilarity of term graphs: two term graphs are said to be bisimilar if they

represent the same term. In [AKP00], suÆcient conditions for|and coun-

terexamples to|con uence, con uence modulo bisimilarity and the Church-

Rosser property modulo bisimilarity of term graph rewriting are established.

Moreover, the paper addresses rewriting modulo bisimilarity, that is, rewriting

of bisimilarity classes of term graphs.

In [HP96] Term Graph Narrowing, which combines term graph rewriting

with �rst-order term uni�cation, is introduced as an approach for solving

equations by transformations on term graphs. The main result is that this

mechanism is complete for all term rewriting systems over which term graph

rewriting is normalizing and con uent. This includes, in particular, all con-

vergent term rewriting systems. The completeness of narrowing strategies for

term graph rewriting is studied in [HP99], where completeness results for three

of the most natural narrowing strategies are established: minimally collapsing,

maximally collapsing, and basic narrowing. The result on basic narrowing im-

proves and corrects a result by Krishna Rao (published in Proc. JICSLP'96 ).

The theory of term graph narrowing is reviewed in [HP02].

6.2 DNA Computing

Ciliates, a very ancient group of organisms, have evolved extraordinary ways

of organizing, manipulating and replicating the DNA in their micronuclear

genomes. The way that ciliates transform genes from their micronuclear (stor-

age) form into their macronuclear (expression) form is very interesting from the

computational point of view. Current research on gene assembly in ciliates is

an example of a ourishing interdisciplinary research involving computer scien-

tists and molecular biologists. On the one hand it belongs to the novel and very

active area of DNA computing where biologists cooperate with computer scien-

tists in designing \computers of the future" based on biomolecules rather than

on silicon. On the other hand it belongs to bioinformatics and computational

biology where computer scientists cooperate with biologists in getting more

understanding of complex biological processes. The model for gene assembly in

ciliates has been presented by us in [EPPR00,EPPR01b,EPR01,PER01]. The

graph transformation aspects of this model concern both the representation

of gene assembly through pointer removal (graph pointer reduction systems,

see [EPPR01b]) and the representation of gene assembly through cyclic graph

decomposition (see [EHR01]). The formal properties of pointer reduction sys-

33

Corradini

tems are also investigated in [EHP+01]. Graph transformation turns out also

to be very useful in de�ning the invariants of the gene assembly processes, see

[EPPR01a].

6.3 Collage Grammars and Picture Generation

The theory of collage grammars represents an interesting use of graph trans-

formation techniques for graphical applications. In [DKL97,DKL01] some

criteria are presented that can be used to disprove context-freeness of collage

languages. Such criteria are of interest because the usual tools like pumping

lemmata fail in the case of collages. Roughly speaking, it is shown that the

number of parts of collages in a context-free collage language grows at most

linearly, and that the volume of parts grows exponentially. Context-free col-

lage and chain-code grammars are compared with respect to their generative

power in [Dre00a]. It is shown that context-free collage grammars based on

similarity transformations can be simulated by context-free chain-code gram-

mars, but that, in general, the language classes generated by both types of

grammars are incomparable.

In [DKK00], context-sensitive and TOL collage grammars are investigated.

Both extensions are shown to enhance the generative power of collage gram-

mars, but while the size of the collages in the language of a TOL collage gram-

mar is bounded exponentially, there is no such bound for context-sensitive

collage languages. In [KKT99], mutually recursive function systems, picture-

generating devices known in the area of fractal geometry, are translated into

TOL collage grammars. The constructed TOL collage grammar yields exactly

those pictures which appear in the in�nite sequence of pictures speci�ed by

the given mutually recursive function system.

A case study on (extensions of) context-free collage grammars is [DK00a],

showing how various types of celtic knotwork can be generated using this type

of grammar, but also indicating some limitations.

While a 2-dimensional grid picture grammar may generate pictures (de-

�ned as subsets of the unit square) with arbitrarily small details, only a �nite

number of them can be made visible as raster images for any given raster.

In [DEKK01], an algorithm based on bottom-up tree automata is presented

which computes the set of all raster images of the pictures generated by a

given grid picture grammar.

In [Dre00b] the concept of tree-based picture generation is introduced. This

yields a uni�ed framework for the generation of pictures that can be extended

to other sorts of objects as well. In the paper it is shown that collage gram-

mars, iterated function systems, chain-code grammars, and 0L-systems with

turtle interpretation are equivalent to natural types of tree-based picture gen-

erators. A tree-based method for the generation of languages of fractals is in-

troduced in [Dre01b]. This combines the nondeterministic nature of grammars

as known from formal language theory with the in�nite re�nement of pictures

34

Corradini

studied in fractal geometry. A system called Treebag which implements the

idea of tree-based object generation is introduced in [Dre98b] (see also http://

www.informatik.uni-bremen.de/theorie/treebag/). Treebag was pre-

sented at several conferences and workshops [Dre98c,DK00b,DK01a].

6.4 Modelling of Mobile Ambients

Paper [FMT01] presents a simple labelled transition system semantics of

Cardelli and Gordon's Ambient calculus. A general and exible model based

on (hyper)graphs is exploited where graph transformation is obtained via (hy-

per)edge replacement and local synchronization with mobility. In addition to

tree-like ambients, the calculus we de�ne works just as well with graph-like

ambients, which are a more realistic model of internetworks.

In [GM01a] a general proposal is presented for mapping processes of calculi

with name mobility into unstructured, non-hierarchical graphs, choosing as

main examples mobile ambients and �-calculus. The �rst step is to prove the

soundness and correctness of the encoding of processes into graphs, in the sense

that two processes are structurally equivalent if and only if the corresponding

graphs are isomorphic. The second is to prove that the encoding is faithful

with respect to the reduction semantics, in the sense that standard graph

rewriting techniques may now be used to simulate reduction steps on processes

by sequences of rewrites on their encodings.

6.5 Modelling of Agent Based Systems

The use of GTS semantics for the formalization of agent-based systems has

been investigated in [KK00a]. An agent system consists of a set of agents and

an environment they can act on. In a graph transformation-based framework,

the environment is of course a graph. In the case of distributed problem

solving, it represents the problem, e.g. a map if we consider a shortest paths

algorithm, that should be solved by the agents. It is also supposed to be a

blackboard for asynchronous communication purposes. In this approach an

agent comprises a set of rules and a �nite automaton. Following the line of

transformation units (see, e.g., [KK99b]), this framework is also independent

of a certain graph transformation approach. The rules are the agents' basic

operational entities to modify its environment. The �nite automaton, here

called capacity, restricts the order in which the rules can be applied.

Two kinds of semantics and their relationships are then considered. The

�rst one is an operational one based on the idea of \enabled" derivations,

while the second one is based on the notion of system states, i.e. con�gura-

tions which consists of an environment combined with a vector of all agents'

control automata states. Based on this approach, it is shown that essential

characteristics of agent systems like reactivity, pro-activity, and cooperation

can easily be modeled using graph transformation.

The idea of a graph transformation-based speci�cation of changes in envi-

35

Corradini

ronments and of agent systems in particular gave rise to further investigations

in the context of logistics management [EK00,EKT00].

6.6 Speci�cation of Control Access Policies

Graph Transformation Systems are exploited in [KMP01b,KMP01a,KMP00,BKPT00]

to provide a uniform and precise framework for the speci�cation of access con-

trol policies. In these approaches, states are represented by graphs and state

transitions by graph transformations. A policy can be formalized by four com-

ponents: a type graph, positive and negative constraints and a set of rules.

This formalism allows the detailed comparison of di�erent policy models and

the precise description of the evolution of a policy and of the integration of

policies.

6.7 Management of semi-structured data and Hypermedia Modeling

Managing semi-structured and unstructured data has recently become the chal-

lenge of database system developers because of the applications (genomic, mul-

timedia, inter/intranet, integration, etc.) concerned. Unstructured databases

can be represented formally by graphs (db-graphs), which entails that query-

ing unstructured data comes down to querying graphs. First order languages

have been investigated [BY98,BY99] in this context. The graph is also one

way to model multi-version and temporal databases (although in that case,

data are graphs of databases and not graphs of data). One diÆcult problem

then is to de�ne complete query languages [BdA99].

In [BtH00], a graph-based hypermedia model is proposed, where hyper-

media dynamics is speci�ed through graph transformation. This approach

addresses the lack of an appropriate language for specifying transformations

of hypermedia networks in known methodologies to hypermedia development.

6.8 Graph Matching

In [VM97] an algorithm for graph matching is presented. It reduces the prob-

lem of �nding a homomorphic image of a pattern graph in a target graph to

that of �nding homomorphic images of every connected component of the pat-

tern in the target. For every connected component, the algorithm performs

a combinatorial search bounded by a pruning operator. The algorithm can

be applied to directed graphs as well as to undirected graphs, and it can also

be specialized to �nd isomorphic images only. In [LV00], an algorithm for

graph pattern matching based on Constraint Satisfaction is presented, and

its eÆciency is demonstrated by the use of a new benchmark for this kind of

algorithms.

36

Corradini

7 Distributed Algorithms based on Graph Relabeling

Systems

Local computations on graphs, as given by graph relabelling systems (with pri-

orities and/or forbidden contexts) are a powerful model for local computations

that can be executed in parallel. Rewriting systems provide a general tool for

encoding distributed algorithms and for proving their correctness. Typically,

one considers a network of processors with arbitrary topology, which is repre-

sented as a connected, undirected graph where vertices denote processors, and

edges denote direct communication links. An algorithm is encoded by means

of local relabellings. Labels attached to vertices and edges are modi�ed lo-

cally, and the relabelling is performed until no more transformation is possible.

Two sequential relabelling steps are said to be independent if they are applied

on disjoint subgraphs: in this case they may be applied in any order or even

concurrently. The papers [MS97a,LMS99] present a general overview of the

approach.

One main thread of research deals with the delimitation of the power of

local computations on graphs with or without some initial knowledge. In

particular, three classical problems are addressed: the recognition problem,

the election problem and the termination detection problem.

The recognition problem asks for computing some topology information

on a network of anonymous processes, assuming some arbitrary extra knowl-

edge about the underlying graph. We introduce a de�nition of recognition

with extra knowledge by means of local relations and we give a necessary and

suÆcient condition for a class of graphs to be recognizable without or with ex-

tra knowledge. These characterizations are based on graphs coverings and on

an algorithm proposed by A. Mazurkievicz. Numerous applications are pre-

sented, in particular concerning minor closed classes of graphs: preliminaries

presentations of this work may be found in [GMM00,MT00a,GM01b].

Using new proof techniques it has been shown in [GMM00] that even know-

ing the number of vertices and/or the number of edges one cannot determine

by using local computations whether a given graph belongs to a certain graph

class like bipartite graphs, graphs having a cut vertex or a cut edge, graphs

having a given graph as minor. Paper [BM98a] presents some algorithms of

enumeration encoded by graph relabelling systems working on 1�graphs. Two

applications are proposed: minor searching and existence of normal forms.

A distributed algorithm terminates whenever it reaches a con�guration in

which no steps of the algorithm can be applied anymore. A local computation

system allows the local detection of (global) termination if for any computation

there is a vertex for which its neighborhood of a given radius r determines

whether or not a normal form has been reached.

In [MM97], �rst a formalization of the local detection problem is presented

and some new methods for obtaining impossibility results are introduced,

based on an extension of the notion of coverings called \quasi-coverings".

37

Corradini

Next it is shown that one cannot detect locally the global termination for

uniformly labelled graphs belonging to certain families of connected graphs,

and the authors address the question whether certain additional knowledge

about a network, which is used in speci�c graph rewriting systems, is really

necessary. For example, they show that election in T -prime graphs is possible

(if and) only if the size of the graph is provided. A characterization of families

of graphs has been obtained in [MT00b] which enables the local detection of

the termination of distributed algorithm.

Sets of random walks on graphs can be formally described by regular ex-

pressions over an alphabet [MS97c,MS97b,MS99]. This provides a powerful

technique to evaluate various parameters related to random walks on graphs,

such as the cover time and the hitting time. An algorithm for generating

random spanning trees in a weighted graph is obtained by considering the

spanning tree de�ned by the edges corresponding to �rst visits to the vertices.

Most distributed algorithms can be modeled as graph model checking or

rewriting algorithms. On the other hand, �xpoint calculi techniques, which

work well for tree-like structures, seem applicable to more complex structures

such as graphs. In such a setting, the general properties of �xpoint calculi for

complete partial orders were investigated in [Jan97a,JW96,Jan97b]. In partic-

ular, an automata-theoretic characterization was obtained. These results may

lead to new insights in the various possible notions of automata or grammars

over graphs.

The Kronecker product of a graph G by K2 is a covering of G: By this

way, we study the following general question: given two connected graphs

whose properties are known, what's happening to these properties when we

do the Kronecker product of these two graphs? We give in [BM98b] results

concerning graph minors, planarity, cut vertex and cut edge.

In [MSZ00], we propose and analyze a randomized algorithm to get ren-

dezvous in an anonymous graph. We examine in particular the probability to

obtain at least one rendezvous and the expected number of rendezvous. We

study the rendezvous number distribution in the cases of chain graphs, rings

and complete graphs. In [MSZ01a], we design and analyze a randomized one-

passage election algorithm in trees based on a result of Angluin. The analysis

models the election process on a tree as an elimination scheme which removes

leaves one by one reducing the tree to a single vertex, called the leader (or

elected vertex). Any leaf whose lifetime has expired is removed. It is assumed

that the lifetimes are independent random variables assigned to vertices as

soon as they become leaves according to some local computable distribution

known at this time. As a particular instance of the model we provide an as-

signment system in a Poisson type random process in which all vertices have

the same chance of being elected. In [MSZ01b] we propose and analyze two

randomized local election algorithms in an asynchronous anonymous graph.

The aim of the \Visualization and simulation of Distributed algorithms"

project is to provide a software tool to help understanding, testing and proving

38

Corradini

distributed algorithms through the visualization of their execution. A �rst

version of the tool has been developed which implement distributed algorithms

described as label rewriting in the sense of M�etivier. It has been presented in

[BMMS02,BGM01b,BGM+01a].

8 Handbooks, Tutorials, and Proceedings

Various contributions by the network participants published during the project

duration are either tutorial introductions to the various approaches to graph

transformation systems, or surveys of results in speci�c research areas. They

witness the e�orts of the participants in training activities.

The volumes [Roz97,EEKR99,EKMR99] form a series of Handbooks about

\Graph Grammars and Computing by Graph Transformation", which address

Foundations, Applications, and Concurrency issues, respectively. The series

is edited by researchers belonging to GETGRATS teams, and many chapters

are authored by members of the network.

The volume on Foundations ([Roz97]) includes chapters about the expres-

sive power of context-free Node Replacement graph grammars [ER97]; Hy-

peredge Replacement, introduced as a context-free method of graph genera-

tion, with emphasis on structural properties as well as on decidability results

[DHK97]; the Algebraic Approaches (both the double- and the single-pushout,

as well as a comparison between the two) [CMR+97,EHK+97]; the Expression

of Graph Properties and of Graph Transformations in Monadic Second-Order

Logic [Cou97a]; and on 2-Structures, seen as a Framework for Decomposition

and Transformation of Graphs [EHR97]).

The volume on Applications, Languages and Tools ([EEKR99]) includes

chapters about Term Graph Rewriting [Plu99b]; applications of Graph Trans-

formation to Visual Languages [BMST99]; picture generation by collage gram-

mars [DK99]; graph transformation units and modules [KK99a]; a view-based

approach to system modeling based on Open Graph Transformation Systems

[HEET99]; the classi�cation and comparison of modularity concepts for graph

transformation systems [EEHT99].

The volume on Concurrency, Parallelism and Distribution includes chap-

ters about Graph relabelling systems and distributed algorithms [LMS99];

Actor Grammars and Local Actions [Jan99]; the Concurrent Semantics of

Algebraic Graph Transformation Systems [BCE+99]; the modeling of Concur-

rent, Mobile and Coordinated Systems via Graph Transformations [MPR99];

Distributed Graph Transformation with Application to Visual Design of Dis-

tributed Systems [FKTV99]; and on High-Level Replacement Systems and

their application to Algebraic Speci�cations and Petri Nets [EGP99].

Other survey papers include [DHK97], which introduces the theory of hy-

peredge replacement as a context-free method of graph generation; [MS97a],

which presents a general overview of graph relabelling systems, [Eng97], on

the expressive power of context-free graph grammars, and [AEH+99], where

39

Corradini

recent developments concerning the application of graph transformation as a

rule-based framework for the speci�cation and development of systems, lan-

guages, and tools are surveyed.

In order to foster the dissemination of the results of the GETGRATS

project, proceedings volumes edited by members of GETGRATS have been

published for the main workshops organized by the network:

� The contributions presented at the \Joint APPLIGRAPH/GETGRATS

Workshop on Graph Transformation", held in Berlin in March 2000 as a

satellite event of the ETAPS 2000 conference, are collected in [ET00], and a

selection of them will appear in special issues of two journals: Mathematical

Structures in Computer Science and Science of Computer Programming.

� The present volume [BC02] contains the proceedings of the \GETGRATS

Closing Workshop", held in Bordeaux in June 2001.

Other proceedings volumes of events sponsored by GETGRATS are [ER98,EEKR00]

(Proceedings of the 6th International Workshop on Theory and Applications

of Graph Transformation (TAGT'98)), and [CH00] (Proceedings of the Work-

shop on Graph Transformation and Visual Modelling Techniques).

References

[AEH+99] M. Andries, G. Engels, A. Habel, B. Ho�mann, H.-J. Kreowski,

S. Kuske, D. Plump, A. Sch�urr, and G. Taentzer. Graph transformation

for speci�cation and programming. Science of Computer Programming,

34(1):1{54, 1999. 8

[AKP97] Z.M. Ariola, J.W. Klop, and D. Plump. Con uent rewriting of

bisimilar term graphs. In Proc. Fourth Workshop on Expressiveness in

Concurrency, volume 7 of Electronic Notes in TCS. Elsevier Science,

1997. 6.1

[AKP00] Z.M. Ariola, J.W. Klop, and D. Plump. Bisimilarity in term graph

rewriting. Inform. and Comput., 156(1/2):2{24, 2000. 6.1

[Bal00] Paolo Baldan. Modelling concurrent computations: from contextual

Petri nets to graph grammars. PhD thesis, Department of Computer

Science, University of Pisa, 2000. Available as technical report n. TD-

1/00. 5.1

[Bal02] Paolo Baldan. Concurrency for graph grammars (in a Petri net shell).

In Bauderon and Corradini [BC02]. This volume. 5.1

[BBCP00a] P. Baldan, N. Busi, A. Corradini, and G.M. Pinna. Domain and

event structure semantics for Petri nets with read and inhibitor

arcs. Technical Report TR-05-00, Department of Computer Science,

University of Pisa, 2000. 5.1

40

Corradini

[BBCP00b] P. Baldan, N. Busi, A. Corradini, and G.M. Pinna. Functorial

concurrent semantics for Petri nets with read and inhibitor arcs. In

C. Palamidessi, editor, CONCUR'00 Conference Proceedings, volume

1877 of LNCS, pages 442{457. Springer, 2000. 5.1

[BC00] M. Bauderon and F. Carrere. Orthogonal graph decompositions. In

Ehrig and Taentzer [ET00], pages 197{204. 2.2

[BC02] M. Bauderon and A. Corradini, editors. Proc. GETGRATS Closing

Workshop, volume 51 of Electronic Notes in TCS. Elsevier Science,

2002. This volume. 8

[BCE+99] P. Baldan, A. Corradini, H. Ehrig, M. L�owe, U. Montanari, and

F. Rossi. Concurrent Semantics of Algebraic Graph Transformation

Systems. In Ehrig et al. [EKMR99], chapter 3. 5.1, 8

[BCEH01] P. Baldan, A. Corradini, H. Ehrig, and R. Heckel. Compositional

modeling of reactive systems using open nets. In K.G. Larsen and

M. Nielsen, editors, Proceedings of CONCUR 2001, volume 2154 of

LNCS, pages 502{518. Springer, 2001. 3.1

[BCK01] P. Baldan, A. Corradini, and B. K�onig. A static analysis technique for

graph transformation systems. In K.G. Larsen and M. Nielsen, editors,

Proceedings of CONCUR 2001, volume 2154 of LNCS, pages 381{395.

Springer, 2001. 5.1

[BCM98] P. Baldan, A. Corradini, and U. Montanari. An unfolding semantics for

DPO graph transformation systems. In Engels and Rozenberg [ER98],

pages 251{260. 5.1

[BCM99] P. Baldan, A. Corradini, and Montanari. Unfolding and Event

Structure Semantics for Graph Grammars. In W. Thomas, editor,

Proceedings FoSSaCS '99, volume 1578 of LNCS, pages 73{89. Springer,

1999. 5.1

[BCM00a] P. Baldan, A. Corradini, and U. Montanari. Contextual Petri nets,

asymmetric event structures and processes. To appear in Information

and Computation. (Also Technical Report TR-99-18 of the Department

of Computer Science, University of Pisa), 2000. 5.1

[BCM00b] P. Baldan, A. Corradini, and U. Montanari. History preserving

bisimulations for contextual nets. In D. Bert and C. Choppy, editors,

WADT'99 Conference Proceedings, volume 1827 of LNCS, pages 291{

310. Springer, 2000. 5.1

[BCM00c] P. Baldan, A. Corradini, and U. Montanari. Unfolding of double-

pushout graph grammars is a core ections. In Ehrig et al. [EEKR00],

pages 145{163. 5.1

[BCM01] P. Baldan, A. Corradini, and U. Montanari. Bisimulation equivalences

for graph grammars. Submitted for publication, 2001. 5.1

41

Corradini

[BdA99] N. Bidoit and S. de Amo. Implicit temporal query languages: towards

completeness. In Proc. of FST&TCS (Chennai { India), 1999. 6.7

[BdMM00a] R. Bruni, D. de Frutos-Escrig, N. Mart��-Oliet, and U. Montanari.

Bisimilarity congruences for open terms and term graphs via tile

logic. In C. Palamidessi, editor, Proceedings of CONCUR 2000, 11th

International Conference on Concurrency Theory, volume 1877 of

LNCS, pages 259{274. Springer, 2000. 3.2

[BdMM00b] R. Bruni, D. de Frutos-Escrig, N. Mart��-Oliet, and U. Montanari. Tile

bisimilarity congruences for open terms and term graphs. Technical

Report TR-00-06, Computer Science Department, University of Pisa,

2000. 3.2

[BE97a] R. Bloem and J. Engelfriet. Characterization of properties and

relations de�ned in monadic second order logic on the nodes of trees.

Tech.Report 97{03, Leiden University, August 1997. 3.3

[BE97b] R. Bloem and J. Engelfriet. Monadic second order logic and node

relations on graphs and trees. In J. Mycielski, G. Rozenberg, and

A. Salomaa, editors, Structures in Logic and Computer Science, volume

1261 of LNCS, pages 144{161. Springer, 1997. 3.3

[BE97c] H.L. Bodlaender and J. Engelfriet. Domino treewidth. J. of

Algorithms, 24:94{123, 1997. 2.10

[BE00] R. Bloem and J. Engelfriet. A comparison of tree transductions de�ned

by monadic second order logic and by attribute grammars. Journal of

Computer and System Sciences, 61:1{50, 2000. 2.6, 3.3

[BG01] R. Bruni and F. Gadducci. Some algebraic laws for spans (and

their connections with multirelations). In W. Kahl, D.L. Parnas, and

G. Schmidt, editors, Proceedings of RelMiS 2001, Relational Methods

in Software, volume 44.3 of Electronic Notes in TCS. Elsevier Science,

2001. 5.3

[BGM99] R. Bruni, F. Gadducci, and U. Montanari. Normal Forms for Partitions

and Relations. In J. L. Fiadeiro, editor, Recent Trends in Algebraic

Development Techniques, volume 1589 of LNCS, pages 31{47. Springer,

1999. 5.3

[BGM+01a] M. Bauderon, S. Gruner, Y. M�etivier, M. Mosbah, and A. Sellami.

Visualization of distributed algorithms based on graph relabelling

systems. In Proceedings GT-VMT 01, volume 50.3 of Electronic Notes

in TCS. Elsevier Science, 2001. 7

[BGM01b] M. Bauderon, S. Gruner, and M. Mosbah. A tool for visualizing

and simulating distributed algorithms. In Procs. Premi�eres Journ�ees

Francophones MODELES FORMELS de l'INTERACTION, 2001. 7

[BGM01c] R. Bruni, F. Gadducci, and U. Montanari. Normal forms for algebras

of connections. Theoret. Comput. Sci., 2001. To appear. 5.3

42

Corradini

[BH01] G. Busatto and B. Ho�mann. Comparing notions of hierarchical graph

transformation. In Workshop on Graph Transformation and Visual

Modelling, Satellite to ICALP'2001, volume 50.3 of Electronic Notes in

TCS. Elsevier Science, 2001. 4.3

[BJ01a] M. Bauderon and H. Jacquet. Categorical product as a generic graph

rewriting mechanism. Applied Categorical Structures, 9(1):65{82, 2001.

2.2

[BJ01b] M. Bauderon and H. Jacquet. Node rewriting in graphs and

hypergraphs: A categorical framework. Theor. Comp. Sci., 266(1-

2):463{487, 2001. 2.2

[BJK02] M. Bauderon, H. Jacquet, and R. Klempien-Hinrichs. Pullback

rewriting and applications. In Bauderon and Corradini [BC02]. This

volume. 2.2

[BKK01] G. Busatto, H.-J. Kreowski, and S. Kuske. Abstract hierarchical graph

transformation. Technical Report 1/01, Universit�at Bremen, 2001. 4.3

[BKPT00] P. Bottoni, M. Koch, F. Parisi Presicce, and G. Taentzer. Consistency

Checking and Visualization of OCL Constraints. In Proc. of UML 2000,

volume 1939 of LNCS. Springer, 2000. 6.6

[BM97] R. Bruni and U. Montanari. Zero-safe nets, or transition

synchronization made simple. In C. Palamidessi and J. Parrow,

editors, Proceedings of EXPRESS'97, 4th workshop on Expressiveness

in Concurrency, volume 7 of Electronic Notes in TCS. Elsevier Science,

1997. 3.2

[BM98a] A. Bottreau and Y. M�etivier. Minors searching, normal forms of graph

rewriting : two applications based on enumeration by graph relabelling.

In Foundations of System Speci�cation and Computation Structures,

volume 1378 of LNCS, pages 110{124. Springer, 1998. 7

[BM98b] A. Bottreau and Y. M�etivier. Some remarks on the kronecker product

of graphs. Information Processing letters, 68:55{61, 1998. 7

[BM98c] R. Bruni and U. Montanari. Zero-safe nets: The individual token

approach. In F. Parisi Presicce, editor, Proceedings of WADT'97,

12th workshop on Recent Trends in Algebraic Development Techniques,

volume 1376 of LNCS, pages 122{140. Springer, 1998. 3.2

[BM99a] R. Bruni and U. Montanari. Cartesian closed double categories, their

lambda-notation, and the pi-calculus. In Proceedings of LICS'99, 14th

Annual IEEE Symposium on Logic in Computer Science, pages 246{

265. IEEE Computer Society Press, 1999. 3.2

[BM99b] R. Bruni and U. Montanari. Zero-safe nets: Composing nets via

transition synchronization. In H. Weber, H. Ehrig, and W. Reisig,

editors, Int. Colloquium on Petri Net Technologies for Modelling

Communication Based Systems, pages 43{80. Fraunhofer Gesellschaft

ISST, 1999. 3.2

43

Corradini

[BM00a] R. Bruni and U. Montanari. Executing transactions in zero-safe nets.

In M. Nielsen and D. Simpson, editors, Proceedings of ICATPN 2000,

21st Int. Conf. on Application and Theory of Petri Nets, volume 1825

of LNCS, pages 83{102. Springer, 2000. 3.2

[BM00b] R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective

and individual token approaches. Inform. and Comput., 156(1{2):46{

89, 2000. 3.2

[BM01a] R. Bruni and U. Montanari. Transactions and zero-safe nets, 2001. To

appear in Advances in Petri nets. 3.2

[BM01b] R. Bruni and U. Montanari. Zero-safe net models for transactions

in linda. In U. Montanari and V. Sassone, editors, Proceedings

of ConCoord 2001, International Workshop on Concurrency and

Coordination, volume 54 of Electronic Notes in TCS. Elsevier Science,

2001. 3.2

[BMM98a] R. Bruni, J. Meseguer, and U. Montanari. Implementing tile systems:

Some examples from process calculi. In P. Degano, U. Vaccaro, and

G. Pirillo, editors, Proceedings of ICTCS'98, 6th Italian Conference on

Theoretical Computer Science, pages 168{179. World Scienti�c, 1998.

3.2

[BMM98b] R. Bruni, J. Meseguer, and U. Montanari. Internal strategies in

a rewriting implementation of tile systems. In C. Kirchner and

H. Kirchner, editors, Proceedings of WRLA'98, 2nd Workshop on

Rewriting Logic and its Applications, volume 15 of Electronic Notes

in TCS. Elsevier Science, 1998. 3.2

[BMM98c] R. Bruni, J. Meseguer, and U. Montanari. Process and term tile

logic. Technical Report SRI-CSL-98-06, SRI International, 1998. Also

Technical Report TR-98-09, Computer Science Department, University

of Pisa. 3.2

[BMM99] R. Bruni, J. Meseguer, and U. Montanari. Executable tile speci�cations

for process calculi. In J.-P. Finance, editor, Proceedings of FASE'99,

Fundamental Approaches to Software Engineering, volume 1577 of

LNCS, pages 60{76. Springer, 1999. 3.2

[BMM01] R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and

cartesian double categories as a semantic framework for tile logic. Math.

Struct. in Comput. Sci., 2001. To appear. 3.2

[BMMS98] R. Bruni, J. Meseguer, U. Montanari, and V. Sassone. A comparison of

petri net semantics under the collective token philosophy. In J. Hsiang

and A. Ohori, editors, Proceedings of ASIAN'98, 4th Asian Computing

Science Conference, volume 1538 of LNCS, pages 225{244. Springer,

1998. 5.6

44

Corradini

[BMMS99] R. Bruni, J. Meseguer, U. Montanari, and V. Sassone. Functorial

semantics for petri nets under the individual token philosophy. In

M. Hofmann, G. Rosolini, and D. Pavlovic, editors, Proceedings of

CTCS'99, 8th Category Theory and Computer Science, volume 29 of

Electronic Notes in TCS. Elsevier Science, 1999. 5.6

[BMMS00] R. Bruni, J. Meseguer, U. Montanari, and V. Sassone. Functorial

models for petri nets. Inform. and Comput., 2000. To appear. 5.6

[BMMS02] M. Bauderon, Y. M�etivier, M. Mosbah, and A. Sellami. Graph

relabelling systems : A tool for encoding, proving, studying and

visualizing distributed algorithms. In Bauderon and Corradini [BC02].

This volume. 7

[BMR01] R. Bruni, U. Montanari, and F. Rossi. An interactive semantics of logic

programming. Theory and Practice of Logic Programming, 2001. To

appear. 3.2

[BMRV99] P. Burmeister, M. Monserrat, F. Rossell�o, and G. Valiente. Algebraic

Transformation of Unary Partial Algebras II: Single-Pushout Approach.

Theoret. Comput. Sci., 216:311{362, 1999. 2.1

[BMS00] R. Bruni, U. Montanari, and V. Sassone. Open ended systems, dynamic

bisimulation and tile logic. In J. van Leeuwen, O. Watanabe, M. Hagiya,

P.D. Mosses, and T. Ito, editors, Proceedings of IFIP TCS 2000, IFIP

Int. Conf. on Theoretical Computer Science, volume 1872 of LNCS,

pages 440{456. Springer, 2000. 3.2

[BMS01] R. Bruni, U. Montanari, and V. Sassone. Dynamic recon�gurability via

tile logic, 2001. Submitted. 3.2

[BMST99] R. Bardhol, M. Minas, A. Sch�urr, and G. Taentzer. Application of

Graph Transformation to Visual Languages. In Ehrig et al. [EEKR99],

chapter 3, pages 105{180. 8

[Bru99] Roberto Bruni. Tile Logic for Synchronized Rewriting of Concurrent

Systems. PhD thesis, Computer Science Department, University of

Pisa, 1999. 3.2

[BS00] R. Bruni and V. Sassone. Algebraic models for contextual nets.

In U. Montanari, J.D.P. Rolim, and E. Welzl, editors, Proceedings

of ICALP 2000, 27th Int. Coll. on Automata, Languages and

Programming, volume 1853 of LNCS, pages 175{186. Springer, 2000.

5.6

[BS01] R. Bruni and V. Sassone. Two algebraic process semantics for

contextual nets, 2001. To appear in Advances in Petri Nets. 5.6

[BtH00] G. Busatto and P.J. 't Hoen. A graph-grammar based approach for

the speci�cation of hypermedia application dynamics. In Rolim et al.

[CH00], pages 403{409. 6.7

45

Corradini

[BY98] N. Bidoit and M. Ykhlef. Fixpoint path queries. In Int. Workshop on

the Web and Databases in conjunction with VI Int. Conf. on Extended

Database Technology, 1998. 6.7

[BY99] N. Bidoit and M. Ykhlef. Fixpoint calculus for querying semistructured

data. In Proc. Int. Workshop on the World Wide Web and Databases,

volume 1590 of LNCS, pages 78{97, 1999. 6.7

[CD97] A. Corradini and F. Drewes. (Cyclic) term graph rewriting is adequate

for rational parallel term rewriting. Technical Report TR-97-14,

Dipartimento di Informatica, Pisa, 1997. 6.1

[CDE+99] M. Clavel, F. Dur�an, S. Eker, N. Mart��-Oliet, J. Meseguer, and

J. Quesada. Maude: Speci�cation and programming in rewriting logic.

SRI International, 1999. Available at http://maude.csl.sri.com/

manual. 3.2

[CG97] A. Corradini and F. Gadducci. A 2-categorical presentation of term

graph rewriting. In Proceedings CTCS'97, volume 1290 of LNCS.

Springer, 1997. 5.3, 5.4

[CG98a] A. Corradini and F. Gadducci. Rational term rewriting. In M. Nivat,

editor, Proceedings FoSSaCS'98, volume 1378 of LNCS, pages 156{171.

Springer, 1998. 5.3

[CG98b] A. Corradini and F. Gadducci. Rewriting on cyclic structures.

Technical Report TR-98-05, Dipartimento di Informatica, Pisa, 1998.

Extended abstract in Proceedings FICS'98. 5.3

[CG99a] A. Corradini and F. Gadducci. An algebraic presentation of term

graphs, via gs-monoidal categories. Applied Categorical Structures,

7:299{331, 1999. 5.3

[CG99b] A. Corradini and F. Gadducci. Functorial Semantics of Multialgebras.

In J. L. Fiadeiro, editor, Recent Trends in Algebraic Development

Techniques, volume 1589 of LNCS. Springer, 1999. 5.3

[CG99c] A. Corradini and F. Gadducci. Rewriting on cyclic structures:

Equivalence between the operational and the categorical description.

Informatique Th�eorique et Applications/Theoretical Informatics and

Applications, 33:467{493, 1999. 5.3

[CG01] A. Corradini and F. Gadducci. A functorial semantics for multi-

algebras and partial algebras, with applications to syntax. Theoret.

Comput. Sci., 2001. To appear. 5.3

[CG02] A. Corradini and F. Gadducci. Categorical Rewriting of Term-like

Structures. In Bauderon and Corradini [BC02]. This volume. 5.3

[CGH99] A. Corradini, M. Gro�e{Rhode, and R. Heckel. An algebra of graph

derivations using �nite (co{) limit double theories. In J. L. Fiadeiro,

editor, Recent Trends in Algebraic Development Techniques, volume

1589 of LNCS, pages 91{105. Springer, 1999. 5.4

46

Corradini

[CGH01] A. Corradini, M. Gro�e{Rhode, and R. Heckel. A coalgebraic

presentation of structured transition systems. Theoret. Comput. Sci.,

260:27 { 55, 2001. 5.5

[CGK00] A. Corradini, F. Gadducci, and W. Kahl. Term graph syntax for multi-

algebras. Technical Report TR-00-04, Dipartimento di Informatica,

2000. 5.3

[CH00] A. Corradini and R. Heckel. Graph transformation and visual

modelling techniques. In J.D.P. Rolim, A.Z. Broder, A. Corradini,

R. Gorrieri, R. Heckel, J. Hromkovic, U. Vaccaro, and J.B.

Wells, editors, ICALP Workshops 2000, volume 8 of Proceedings in

Informatics, pages 357{486. Carleton Scienti�c, 2000. 8

[CHM99a] A. Corradini, R. Heckel, and U. Montanari. From SOS Speci�cations

to Structured Coalgebras: How to Make Bisimulation a Congruence.

In B. Jacobs and J. Rutten, editors, Coalgebraic Methods in Computer

Science '99, volume 19 of Electronic Notes in TCS. Elsevier Science,

1999. 5.5

[CHM99b] A. Corradini, R. Heckel, and U. Montanari. Tile transition systems

as structured coalgebras. In G. Ciobanu and Gh. Paun, editors,

Fundamentals of Computation Theory, volume 1684 of LNCS, pages

13{38. Springer Verlag, 1999. 5.5

[CHM00] A. Corradini, R. Heckel, and U. Montanari. Graphical Operational

Semantics. In Rolim et al. [CH00], pages 357{486. 3.6

[CHM01] A. Corradini, R. Heckel, and U. Montanari. Compositional SOS and

beyond: A coalgebraic view of open systems. Technical Report TR-01-

01, Dipartimento di Informatica, Universit�a di Pisa, 2001. To appear

in TCS. 5.5

[CL98] B. Courcelle and D. Lapoire. Facial circuits of planar graphs and

context-free languages. In L. Brim, J. Gruska, and J. Zlatu�ska, editors,

Proc. of Mathematical Foundations of Computer Science 1998, volume

1450 of LNCS. Springer, 1998. 3.3

[CM00] B. Courcelle and J.A. Makowsky. Operations on relational structures

and their compatibility with monadic second-order logic. In Ehrig and

Taentzer [ET00], pages 206{214. 2.3

[CM01] B. Courcelle and J.A. Makowsky. Fusion in relational structures and

the veri�cation of monadic second-order properties. Math. Struct. in

Comput. Sci., 2001. To appear. 3.3

[CMR+97] A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. L�owe.

Algebraic Approaches to Graph Transformation I: Basic Concepts and

Double Pushout Approach. In Rozenberg [Roz97], chapter 3. 2.1, 8

[CMR99] B. Courcelle, J.A. Makowsky, and U. Rotics. Linear time solvable

optimization problems on certain graph families. In Proc. 24th

47

Corradini

Intl. Workshop on Graph-Theoretic Concepts in Computer Science

(WG'98), volume 1517 of LNCS, pages 1{16, 1999. 3.3

[CMR00] B. Courcelle, J.A. Makowsky, and U. Rotics. Linear time solvable

optimization problems on certain structured graph families. Theory of

Computer Science (formerly Mathematical Systems Theory), 33:125{

150, 2000. 3.3

[CMR01] B. Courcelle, J.A. Makowsky, and U. Rotics. On the �xed parameter

complexity of graph enumeration problems de�nable in monadic second

order logic. Discrete Applied Mathematics, 108:23{52, 2001. 3.3

[CO00] B. Courcelle and S. Olariu. Upper bounds to the clique-width of graphs.

Discrete Applied Mathematics, 101:77{114, 2000. 3.3

[Cor93] Andrea Corradini. Term rewriting in CT�. In Proceedings CAAP '93,

volume 668 of LNCS, pages 468{484. Springer, 1993. 5.3

[Cou96a] Bruno Courcelle. Basic notions of universal algebra for language theory

and graph grammars. Theoret. Comput. Sci., 163:1{54, 1996. 3.3

[Cou96b] Bruno Courcelle. The monadic second-order logic of graphs X: Linear

orders. Theoret. Comput. Sci., 160:87{143, 1996. 3.3

[Cou97a] Bruno Courcelle. The expression of graph properties and graph

transformations in monadic second-order logic. In Rozenberg [Roz97],

chapter 5. 8

[Cou97b] Bruno Courcelle. On the expression of graph properties in some

fragments of monadic second-order logic. In N. Immerman and

P. Kolaitis, editors,Descriptive complexity and �nite models, volume 31,

pages 33{62. DIMACS Series in Discrete Mathematics and Theoretical

Computer Sciences, June 1997. 3.3

[Cou99] Bruno Courcelle. The monadic second-order logic of graphs XI:

Hierarchical decompositions of connected graphs. Theoret. Comput.

Sci., 224:35{58, 1999. 3.3

[Cou00a] Bruno Courcelle. Graph operations and monadic second-order logic:

a survey. In Proceedings Logic for Programming and Automated

Reasoning (LPAR), volume 1955 of LNCS, pages 20{24. Springer, 2000.

3.3

[Cou00b] Bruno Courcelle. The monadic second-order logic of graphs XII: Planar

graphs and planar maps. Theoret. Comput. Sci., 237:1{32, 2000. 3.3

[Cou00c] Bruno Courcelle. The monadic second-order logic of graphs XIII:

Graph drawings with edge crossings. Theoret. Comput. Sci., 244:63{94,

2000. 3.3

[Cou01a] Bruno Courcelle. Graphs, Trees and Monadic Second-Order Logic, Part

I : Tutorial, Part II : Recent results and open problems. In Proceedings

8th Workshop on Logic, Language, Information and Computation, 2001.

3.3

48

Corradini

[Cou01b] Bruno Courcelle. A monadic second-order de�nition of the structure of

convex hypergraphs. Inform. and Comput., 2001. To appear. 3.3

[Cou01c] Bruno Courcelle. The monadic second-order logic of graphs XIV:

Uniformly sparse graphs and edge set quanti�cations. Theoret.

Comput. Sci., 2001. To appear. 3.3

[DE98] F. Drewes and J. Engelfriet. Decidability of the �niteness of ranges of

tree transductions. Inform. and Comput., 145:1{50, 1998. 2.6

[DEKK01] F. Drewes, S. Ewert, R. Klempien-Hinrichs, and H.-J. Kreowski.

Computing raster images from grid picture grammars. In S. Yu,

editor, Proc. 5th Intl. Conference on Implementation and Application

of Automata (CIAA 2000), volume 2088 of LNCS. Springer, 2001. 6.3

[DHK97] F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement

graph grammars. In Rozenberg [Roz97], chapter 2. 8

[DHP01] F. Drewes, B. Ho�mann, and D. Plump. Hierarchical graph

transformation. Journal of Computer and System Sciences, 2001. To

appear. 4.3

[DK99] F. Drewes and H.-J. Kreowski. Picture generation by collage grammars.

In Ehrig et al. [EEKR99], chapter 11, pages 397{457. 8

[DK00a] F. Drewes and R. Klempien-Hinrichs. Picking knots from trees. The

syntactic structure of celtic knotwork. In M. Anderson, P. Cheng,

and V. Haarslev, editors, Proc. 1st Intl. Conference on Theory and

Application of Diagrams 2000, volume 1889 of Lecture Notes in

Arti�cial Intelligence, pages 89{104. Springer, 2000. 6.3

[DK00b] F. Drewes and P. Knirsch. Treebag { a short presentation. In Nagl

et al. [NSM00], pages 411{417. 6.3

[DK01a] F. Drewes and R. Klempien-Hinrichs. Treebag. In M. Daley,

M.G. Eramian, and S. Yu, editors, Proc. 5th Intl. Conference on

Implementation and Application of Automata (CIAA 2000), volume

2088 of LNCS. Springer, 2001. 6.3

[DK01b] F. Drewes and H.-J. Kreowski. Reading words in graphs generated by

hyperedge replacement. In C. Martin-Vide and V. Mitrana, editors,

Where Mathematics, Computer Science, Linugistics and Biology meet,

pages 243{252. Kluwer Academic Publishers, 2001. 2.3

[DKK00] F. Drewes, R. Klempien-Hinrichs, and H.-J. Kreowski. Table-

driven and context-sensitive collage languages. In G. Rozenberg

and W. Thomas, editors, Proc. Developments in Language Theory

(DLT'99), pages 326{337. World Scienti�c, 2000. 6.3

[DKKK00] F. Drewes, P. Knirsch, H.-J. Kreowski, and S. Kuske. Graph

transformation modules and their composition. In Nagl et al. [NSM00],

pages 15{30. 4.4

49

Corradini

[DKL97] F. Drewes, H.-J. Kreowski, and D. Lapoire. Criteria to disprove

context-freeness of collage languages. In B.S. Chlebus and L. Czaja,

editors, Proc. Fundamentals of Computation Theory XI, volume 1279

of LNCS, pages 169{178. Springer, 1997. 6.3

[DKL01] F. Drewes, H.-J. Kreowski, and D. Lapoire. Criteria to disprove

context-freeness of collage languages. Theoret. Comput. Sci., 2001. To

appear. 6.3

[Dre97] Frank Drewes. On the generation of trees by hyperedge replacement.

In I. Pr��vara and P. Ru�zi�cka, editors, Proc. Mathematical Foundations

of Computer Science 1997, volume 1295 of LNCS, pages 229{238.

Springer, 1997. 2.3

[Dre98a] Frank Drewes. A characterization of the sets of hypertrees generated

by hyperedge-replacement graph grammars. Theory of Computing

Systems, 32:159{208, 1998. 2.3

[Dre98b] Frank Drewes. Treebag|a tree-based generator for objects of various

types. Report 1/98, Univ. Bremen, 1998. 6.3

[Dre98c] Frank Drewes. Treebag { Baum-basierte Generierung und

Transformation von Objekten. In J. Dassow and R. Kruse, editors,

Proc. Informatik '98, Informatik Aktuell, pages 47{56, 1998. In

German. 6.3

[Dre99] Frank Drewes. The complexity of the exponential output size problem

for top-down tree transducers. In G. Ciobanu and Gh. P�aun, editors,

Proc. Fundamentals of Computation Theory (FCT'99), volume 1684 of

LNCS, pages 234{245. Springer, 1999. 2.6

[Dre00a] Frank Drewes. Some remarks on the generative power of collage

grammars and chain-code grammars. In Ehrig et al. [EEKR00], pages

1{14. 6.3

[Dre00b] Frank Drewes. Tree-based picture generation. Theoret. Comput. Sci.,

246:1{51, 2000. 6.3

[Dre01a] Frank Drewes. The complexity of the exponential output size problem

for top-down and bottom-up tree transducers. Inform. and Comput.,

2001. To appear. 2.6

[Dre01b] Frank Drewes. Tree-based generation of languages of fractals. Theoret.

Comput. Sci., 262:377{414, 2001. 6.3

[EEHT97] G. Engels, H. Ehrig, R. Heckel, and G. Taentzer. A combined reference

model- and view-based approach to system speci�cation. International

Journal of Software Engineering and Knowledge Engineering, 7(4):457{

477, 1997. 3.1

[EEHT99] H. Ehrig, G. Engels, R. Heckel, and G. Taentzer. Classi�cation and

comparison of modularity concepts for graph transformation systems.

In Ehrig et al. [EEKR99], chapter 17. 8

50

Corradini

[EEKR99] H. Ehrig, G. Engels, H.-J. Kreowski, and

G. Rozenberg, editors. Handbook of Graph Grammars and Computing

by Graph Transformation. Vol. 2: Applications, Languages, and Tools.

World Scienti�c, 1999. 8

[EEKR00] H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors.

Proceedings of Workshop on Theory and Application of Graph

Transformations (TAGT'98), Paderborn, Germany, November 1998,

volume 1764 of LNCS. Springer, 2000. 8

[EGP99] H. Ehrig, M. Gajewsky, and F. Parisi Presicce. High-Level Replacement

Systems Applied to Algebraic Speci�cations and Petri Nets. In Ehrig

et al. [EKMR99], chapter 6, pages 341{399. 2.4, 8

[EH99] J. Engelfriet and H.J. Hoogeboom. Tree-walking pebble automata. In

J. Karhum�aki, H. Maurer, G. Paun, and G. Rozenberg, editors, Jewels

are forever, contributions to Theoretical Computer Science in honor of

Arto Salomaa, pages 72{83. Springer, 1999. 3.3

[EHHR00a] A. Ehrenfeucht, J. Hage, T. Harju, and G. Rozenberg. Complexity

issues in switching classe of graphs. In Ehrig et al. [EEKR00], pages

59{70. 2.7

[EHHR00b] A. Ehrenfeucht, J. Hage, T. Harju, and G. Rozenberg. Pancyclicity in

switching classes. Information Processing Letters, 73(5{6):153 { 156,

2000. 2.7

[EHK+97] H. Ehrig, R. Heckel, M. Kor�, M. L�owe, L. Ribeiro, A. Wagner, and

A. Corradini. Algebraic approaches to graph transformation II: Single

pushout approach and comparison with double pushout approach. In

Rozenberg [Roz97], chapter 4. 2.1, 8

[EHL+00] H. Ehrig, R. Heckel, M. Llabres, F. Orejas, J. Padberg, and

G. Rozenberg. Double-Pullback Graph Transitions: A Rule-Based

Framework with Incomplete Information. In Ehrig et al. [EEKR00],

pages 85{102. 3.1

[EHP+01] A. Ehrenfeucht, T. Harju, I. Petre, D.M. Prescott, and G. Rozenberg.

Formal systems for gene assembly in ciliates. Theoret. Comput. Sci.,

2001. To appear. 6.2

[EHP02] H. Ehrig, A. Habel, and F. Parisi Presicce. Basic Results for Two

Types of High-Level Replacement Systems. In Bauderon and Corradini

[BC02]. This volume. 2.4

[EHR97] A. Ehrenfeucht, T. Harju, and G. Rozenberg. The theory of 2-

structures: A framework for decomposition and transformation of

graphs. In Rozenberg [Roz97], chapter 6. 2.7, 8

[EHR01] A. Ehrenfeucht, T. Harju, and G. Rozenberg. Gene assembly through

cyclic graph decomposition. Theoret. Comput. Sci., 2001. To appear.

6.2

51

Corradini

[EHTE97] G. Engels, R. Heckel, G. Taentzer, and H. Ehrig. A view-oriented

approach to system modelling using graph transformation. In Proc. of

ESEC/FSE'97, Z�urich, volume 1301 of LNCS, pages 327{343. Springer,

1997. 3.1

[EHvB99] J. Engelfriet, H.J. Hoogeboom, and J.-P. van Best. Trips on trees. Acta

Cybernetica, pages 51{64, 1999. 3.3

[EK00] J. Eschenb�acher and P. Knirsch. Reengineering of supply chain

networks with change management. In Global Logistics for the New

Millennium { Proc. of the 5th Internat. Symposium on Logistics (ISL

2000), Iwate, Japan, pages 198{207, 2000. 6.5

[EKMR99] H. Ehrig, H.-J. Kreowski, U. Montanari, and G. Rozenberg,

editors. Handbook of Graph Grammars and Computing by Graph

Transformation. Vol. 3: Concurrency, Parallelism, and Distribution.

World Scienti�c, 1999. 8

[EKT00] J. Eschenb�acher, P. Knirsch, and I.J. Timm. Demand chain

optimisation by using agent technology. In IFIP WG 5.7 {

International Conference on Integrated Production Management:

Information and Communication Technology in Logistics and

Production Management, Tromso, Norway, pages 285{292, 2000. 6.5

[EM99] J. Engelfriet and S. Maneth. Macro tree transducers, attribute

grammars, and MSO de�nable tree translations. Inform. and Comput.,

154:34{91, 1999. 2.6

[EM00a] J. Engelfriet and S. Maneth. Characterizing and deciding MSO-

de�nability of macro tree transductions. In H. Reichel and S. Tison,

editors, Proceedings STACS'2000, volume 1770 of LNCS, pages 542{

554, Berlin, 2000. Springer. 2.6

[EM00b] J. Engelfriet and S. Maneth. Tree languages generated by context-free

graph grammars. In Ehrig et al. [EEKR00]. 2.6

[EM01] J. Engelfriet and S. Maneth. Macro tree translations of linear size

increase are MSO de�nable. Technical Report 01-08, LIACS, Leiden

University, 2001. 2.6

[Eng97] J. Engelfriet. Context-free graph grammars. In G. Rozenberg and

A. Salomaa, editors, Handbook of Formal Languages, volume 3: Beyond

Words. Springer, 1997. 8

[EO01] H. Ehrig and F. Orejas. Integration Paradigm for Data Type and

Process Speci�cation Techniques . In G. Paun, G. Rozenberg, and

A. Salomaa, editors, Current Trends in Theoretical Computer Science:

Entering the 21st Century, pages 192 { 201. World Scienti�c, Singapore,

2001. 3.5

[EPO01] H. Ehrig, J. Padberg, and F. Orejas. From Basic Views and Aspects

to Integration of Speci�cation Formalisms . In G. Paun, G. Rozenberg,

52

Corradini

and A. Salomaa, editors, Current Trends in Theoretical Computer

Science: Entering the 21st Century, pages 202 { 214. World Scienti�c,

Singapore, 2001. 3.5

[EPPR00] A. Ehrenfeucht, I. Petre, D.M. Prescott, and G. Rozenberg. Universal

and simple operations for gene assembly in ciliates. In V. Mitrana

and C. Martin-Vide, editors, Words, Sequences, Languages: Where

computer science, biology and linguistics come across, 2000. To appear.

6.2

[EPPR01a] A. Ehrenfeucht, I. Petre, D.M. Prescott, and G. Rozenberg. Circularity

and other invariants of gene assembly in ciliates. Submitted for

publication, 2001. 6.2

[EPPR01b] A. Ehrenfeucht, I. Petre, D.M. Prescott, and G. Rozenberg. String and

graph reduction systems for gene assembly in ciliates. Math. Struct. in

Comput. Sci., 2001. To appear. 6.2

[EPR01] A. Ehrenfeucht, D.M. Prescott, and G. Rozenberg. Computational

aspects of gene (un)scrambling in ciliates. In L. Landweber and

E. Winfree, editors, Evolution as Computation, pages 45{86. Springer,

2001. 6.2

[ER97] J. Engelfriet and G Rozenberg. Node Replacement Graph Grammars.

In Rozenberg [Roz97], chapter 1. 8

[ER98] G. Engels and G. Rozenberg, editors. Preliminary Proc. 6th Int.

Workshop on Theory and Applications of Graph Transformation

(TAGT'98, number tr{ri{98{201 in Reihe Informatik. Universit�at{

Gesamthochschule Paderborn, 1998. 8

[ERP98] H. Ehrig, G. Rozenberg, and J. Padberg. Graph transformations and

other rule-based formalisms with incomplete information. In Engels

and Rozenberg [ER98], pages 268{278. 3.1

[ET00] H. Ehrig and G. Taentzer, editors. Proceedings of Joint

APPLIGRAPH/GETGRATS Workshop on Graph Transformation

(GRATRA 2000). Technical Report No. 2000-2, FB Informatik, TU

Berlin, April 2000. 8

[EV98] J. Engelfriet and H. Vogler. The equivalence of bottom-up and top-

down tree-to-graph transducers. J. of Comput. System Sci., 56:332{

356, 1998. 2.6

[FKT00] I. Fischer, M. Koch, and G. Taentzer. Local views on distributed

systems and their communications. In Ehrig et al. [EEKR00], pages

164{178. 4.1

[FKTV99] I. Fischer, M. Koch, G. Taentzer, and V. Volle. Distributed graph

transformation with application to visual design of distributed systems.

In Ehrig et al. [EKMR99], chapter 5. 4.1, 8

53

Corradini

[FMT01] G. Ferrari, U. Montanari, and E. Tuosto. A LTS Semantics of Ambients

via Graph Synchronization with Mobility. In Proceedings ICTCS 2001,

volume 2202 of LNCS. Springer, 2001. 6.4

[GEMT00a] M. Goedicke, B. Endres, T. Meyer, and G. Taentzer. Tool support

for viewpoint-oriented software development: Towards integration of

multiple perspectives by distributed graph transformation. In Nagl

et al. [NSM00], pages 369{378. 4.1

[GEMT00b] M. Goedicke, B. Endres, T. Meyer, and G. Taentzer. Viewpoint-

oriented software development: Tool support for integrating multiple

perspectives by distributed graph transformation. In Proceedings 6th

Int. Conf. on Tools and Algorithms for the Construction and Analysis

of Systems, volume 1785, pages 43{47. Springer, 2000. 4.1

[GH98] F. Gadducci and R. Heckel. An inductive view of graph transformation.

In F. Parisi Presicce, editor, Recent Trends in Algebraic Development

Techniques, volume 1376 of LNCS, pages 219{233. Springer, 1998. 5.4

[GHK00] F. Gadducci, R. Heckel, and M. Koch. A fully abstract model for

graph-interpreted temporal logic. In Ehrig et al. [EEKR00]. 3.4

[GHL99] F. Gadducci, R. Heckel, and L. Llabr�es. A bi-categorical axiomatisation

of concurrent graph rewriting. In M. Hofmann, D. Pavlovi�c, and

P. Rosolini, editors, Proc. 8th Conference on Category Theory and

Computer Science (CTCS'99), Edinburgh, UK, volume 29 of Electronic

Notes in TCS. Elsevier Science, September 1999. 5.4

[GM00] F. Gadducci and U. Montanari. The tile model. In G. Plotkin,

C. Stirling, and M. Tofte, editors, Proof, Language and Interaction:

Essays in Honour of Robin Milner. MIT Press, 2000. Also Technical

Report TR-27/96, Dipartimento di Informatica, Universit�a di Pisa,

1996. 3.2

[GM01a] F. Gadducci and U. Montanari. A concurrent graph semantics for

mobile ambients. In S. Brookes and M. Mislove, editors, Mathematical

Foundations of Programming Semantics, volume 45 of Electronic Notes

in TCS. Elsevier Science, 2001. Available at http://www.elsevier.

nl/locate/entcs/volume45.html/. 6.4

[GM01b] E. Godard and Y. M�etivier. A characterization of classes of graphs

recognizable by local computations with initial knowledge. In Proc. 8th

International colloquium on structural information and communication

complexity, pages 179{193. Carleton scienti�c, 2001. 7

[GMM00] E. Godard, Y. M�etivier, and A. Muscholl. The power of local

computations in graphs with initialknowledge. In Ehrig et al.

[EEKR00], pages 71{84. 7

[GMT99] M. Goedicke, T. Meyer, and G. Taentzer. Viewpoint-oriented software

development by distributed graph transformation: Towards a basis for

54

Corradini

living with inconsistencies. In Proceedings 4th IEEE International

Symposium on Requirements Engineering (RE'99), pages 43{47. IEEE

Computer Society, 1999. ISBN 0-7695-0188-5. 4.1

[GPS97] M. Gro�e{Rhode, F. Parisi Presicce, and M. Simeoni. A simple notion

of re�nement in graph transformation systems. Report 10/97, Univ.

Roma 'La Sapienza', 1997. 4.5

[GPS98] M. Gro�e{Rhode, F. Parisi Presicce, and M. Simeoni. Spatial and

temporal re�nement of typed graph transformation systems. In

L. Brim, J. Gruska, and J. Zlatu�ska, editors, Proc. of Mathematical

Foundations of Computer Science 1998, volume 1450 of LNCS, pages

553{561. Springer, 1998. 4.5

[GPS00] M. Gro�e{Rhode, F. Parisi Presicce, and M. Simeoni. Re�nements of

Graph Transformation Systems via Rule Expressions. In Ehrig et al.

[EEKR00], pages 368{382. 4.5

[GPS01] M. Gro�e{Rhode, F. Parisi Presicce, and M. Simeoni. Formal

software speci�cation with re�nement and modules for typed graph

transformation systems. J. Computer and System Science, 2001. To

appear. 4.5

[GPST00] M. Gro�e{Rhode, F. Parisi Presicce, M. Simeoni, and G. Taentzer.

Modeling Distributed Systems by Modular Graph Transformation

based on Re�nement via Rule Expressions. In Nagl et al. [NSM00],

pages 31{45. 4.5

[Gro98] Martin Gro�e{Rhode. Algebra Transformation Systems and their

Composition. In E. Astesiano, editor, Fundamental Approaches to

Software Engineering (FASE'98), volume 1382 of LNCS, pages 107{

122. Springer, 1998. 2.5, 4.1

[Gro02] Martin Gro�e{Rhode. Algebra Transformation Systems as a Unifying

Framework. In Bauderon and Corradini [BC02]. This volume. 2.5

[Gru00a] Stefan Gruner. A combined graph schema and graph grammar

approach to consistency in distributed data modeling. In Nagl et al.

[NSM00]. 3.6

[Gru00b] Stefan Gruner. Meta-Typing is Compatible to the Typed SPO

Approach. In Ehrig and Taentzer [ET00], pages 50{58. 2.1

[GSP99] M. Gro�e{Rhode, M. Simeoni, and F. Parisi Presicce. Re�nements and

Modules for Typed Graph Transformation Systems. In J. L. Fiadeiro,

editor, Proceedings of WADT'98, 13th Workshop on Recent Trends in

Algebraic Development Techniques, volume 1589 of LNCS. Springer,

1999. 4.5

[Hag99] J. Hage. The membership problem for switching classes with skew

gains. Fundamenta Informaticae, 39(4):375{387, 1999. 2.7

55

Corradini

[Hag01] J. Hage. Structural Aspects Of Switching Classes. PhD thesis, LIACS,

Leiden University, 2001. 2.7

[Hec98a] Reiko Heckel. Compositional veri�cation of reactive systems speci�ed

by graph transformation. In Proc. Fundamental Approaches to Software

Engineering, volume 1382 of LNCS, pages 138{153. Springer, 1998. 3.1

[Hec98b] Reiko Heckel. Open Graph Transformation Systems: A New Approach

to the Compositional Modelling of Concurrent and Reactive Systems.

PhD thesis, Technical University of Berlin, Dep. of Comp. Sci., 1998.

3.1, 3.4, 5.4

[HEET99] R. Heckel, H. Ehrig, G. Engels, and G. Taentzer. A view-based

approach to system modeling based on open graph transformation

systems. In Ehrig et al. [EEKR99], chapter 16, pages 639{668. 3.1, 8

[HEWC97] R. Heckel, H. Ehrig, U. Wolter, and A. Corradini. Integrating the

speci�cation techniques of graph transformation and temporal logic. In

Proc. of MFCS'97, Bratislava, volume 1295 of LNCS. Springer, 1997.

3.1

[HEWC01] R. Heckel, H. Ehrig, U. Wolter, and A. Corradini. Double-pullback

transitions and coalgebraic loose semantics for graph transformation

systems. Applied Categorical Structures, 9(1), 2001. See also TR 97-

07 at http://www.cs.tu-berlin.de/cs/ifb/TechnBerichteListe.

html. 3.1

[HH98] J. Hage and T. Harju. Acyclicity of switching classes. Europan J.

Combin., 19:321 { 327, 1998. 2.7

[HH00] J. Hage and T. Harju. The size of switching classes with skew gains.

Discrete Mathematics, 215:81 { 92, 2000. 2.7

[HH01] J. Hage and T. Harju. A characterization of acyclic switching classes

using forbidden subgraphs. Technical Report 5, Leiden University,

Department of Computer Science, 2001. Submitted to European J.

Combin. 2.7

[HHKK00] R. Heckel, B. Ho�mann, P. Knirsch, and S. Kuske. Simple modules for

grace. In Ehrig et al. [EEKR00], pages 383{395. 4.4

[HIM98] D. Hirsch, P. Inverardi, and U. Montanari. Graph grammars and

constraint solving for software architecture styles. In Proceedings

ISAW'98, 1998. 4.2

[HIM99] D. Hirsch, P. Inverardi, and U. Montanari. Modeling software

architectures and styles with graph grammars and constraint solving.

In Proc. Working IFIP Conference on Software Architecture, 1999. 4.2

[HIM00] D. Hirsch, P. Inverardi, and U. Montanari. Recon�guration of software

architecture styles with name mobility. In A. Porto and G.-C. Roman,

editors, Coordination 2000, volume 1906 of LNCS, pages 148{163.

Springer, 2000. 4.2

56

Corradini

[HK98] A. Habel and R. Klempien-Hinrichs. Atom replacement in hypergraphs.

In Engels and Rozenberg [ER98], pages 182{189. 2.3

[HM99] D. Hirsch and U. Montanari. Consistent transformations for software

architecture styles of distributed systems. In Proc. Workshop on

Distributed Systems, volume 28 of Electronic Notes in TCS. Elsevier

Science, 1999. 4.2

[HM00] D. Hirsch and U. Montanari. Higher-order hyperedge replacement

systems and their transformations. In Ehrig and Taentzer [ET00], pages

215{223. 4.2

[HM01a] D. Hirsch and U. Montanari. A Graphical Calculus for Name Mobility.

In Proceedings Workshop on Software Engineering and Mobility, co-

located with ICSE 2001, 2001. 4.2

[HM01b] D. Hirsch and U. Montanari. Synchronized hyperedge replacement with

name mobility. In K.G. Larsen and M. Nielsen, editors, Proceedings of

CONCUR 2001, volume 2154 of LNCS, pages 121{136. Springer, 2001.

4.2

[HMP00] A. Habel, J. M�uller, and D. Plump. Double-pushout approach with

injective matching. In Ehrig et al. [EEKR00], pages 103{116. 2.1

[HMP01] A. Habel, J. M�uller, and D. Plump. Double-pushout graph

transformation revisited. Math. Struct. in Comput. Sci., 11(5):637{

688, 2001. 2.1

[HP96] A. Habel and D. Plump. Term graph narrowing. Math. Struct. in

Comput. Sci., 6:649{676, 1996. 6.1

[HP99] A. Habel and D. Plump. Complete strategies for term graph narrowing.

In Recent Developments in Algebraic Development Techniques, Selected

Papers, volume 1589 of LNCS, pages 152{167. Springer, 1999. 6.1

[HP01] A. Habel and D. Plump. Computational completeness of programming

languages based on graph transformation. In Proc. Foundations of

Software Science and Computation Structures (FoSSaCS 2001), volume

2030 of LNCS, pages 230{245. Springer, 2001. 2.9

[HP02] A. Habel and D. Plump. Solving equations by graph transformation.

In Bauderon and Corradini [BC02]. This volume. 6.1

[Jan97a] D. Janin. Automata, tableaux and a reduction theorem for �xpoint

calculi in arbitrary complete lattices. In IEEE Symp. on Logic in

Computer Science, 1997. 7

[Jan97b] D. Janin. When the satis�ability problem for �xpoint expressions in

complete ordered sets is simple. In CSL'97, 1997. Submitted to the

proceedings. 7

[Jan99] Dirk Janssens. Actor grammars and local actions. In Ehrig et al.

[EKMR99], chapter 2. 5.2, 8

57

Corradini

[Jan02] Dirk Janssens. Processes and local actions. In Bauderon and Corradini

[BC02]. This volume. 5.2

[JK00] H. Jacquet and R. Klempien-Hinrichs. Node replacement in

hypergraphs: Translating NCE rewriting into the pullback approach.

In Ehrig et al. [EEKR00], pages 117{130. 2.2

[JL99] D. Janin and G. Lenzi. On the structure of monadic logic of the

binary tree. In Proc. 24th Int. Symp. on Mathematical Foundations

of Computer Science, volume 1672 of LNCS, pages 310{320. Springer,

1999. 3.3

[JM96] D. Janssens and T. Mens. Abstract semantics for ESM systems.

Fundamenta Informaticae, 26:315{339, 1996. 5.2

[JV99] D. Janssens and N. Verlinden. Algebraic properties of LAS processes.

Technical report, Universiteit Antwerpen, UIA, 1999. 5.2

[JV00] D. Janssens and N. Verlinden. A framework for NLC and ESM: Local

Action Systems. In Ehrig et al. [EEKR00], pages 194{214. 5.2

[JV01] D. Janssens and N. Verlinden. Modeling petri nets by local action

systems. In GT-VMT 2001 Proceedings, volume 50.3 of Electronic

Notes in TCS. Elsevier Science, 2001. 5.2

[JW96] D. Janin and I. Walukiewicz. On the expressive completeness of

the modal mu-calculus w.r.t. monadic second order logic. In Proc.

CONCUR'96, volume 1119 of LNCS, 1996. 7

[KK99a] H.-J. Kreowski and S. Kuske. Graph Transformation Unitis and

Modules. In Ehrig et al. [EEKR99], chapter 15, pages 607{638. 8

[KK99b] H.-J. Kreowski and S. Kuske. Graph transformation units with

interleaving semantics. Formal Aspects of Computing, 11(6):690{723,

1999. 4.4, 6.5

[KK00a] P. Knirsch and H.-J. Kreowski. A note on modeling agent systems by

graph transformation. In Nagl et al. [NSM00], pages 411{417. 6.5

[KK00b] H. Kreowski and S. Kuske. Suggestions on the modularization of

rule-based systems. In Martin Wirsing, Martin Gogolla, Hans-J�org

Kreowski, Tobias Nipkow, and Wolfgang Reif, editors, Proc. Rigorose

Entwicklung software-intensiver Systeme, Technical Report Nr. 0005,

University of Munich, pages 73{82, 2000. 4.4

[KK00c] H.-J. Kreowski and S. Kuske. Note on approach-independent

structuring concepts for rule-based systems. In Ehrig and Taentzer

[ET00], pages 41{49. 4.4

[KKS97] H.-J. Kreowski, S. Kuske, and A. Sch�urr. Nested graph transformation

units. International Journal of Software Engineering and Knowledge

Engineering, 7(4):479{502, 1997. 4.4

58

Corradini

[KKT99] R. Klempien-Hinrichs, H.-J. Kreowski, and S. Taubenberger. Correct

translation of mutually recursive function systems into TOL collage

grammars. In G. Ciobanu and Gh. P�aun, editors, Proc. 12th

Intl. Symposium on Fundamentals of Computation Theory (FCT'99),

volume 1684 of LNCS, pages 350{361. Springer, 1999. 6.3

[Kle98] Renate Klempien-Hinrichs. Net re�nement by pullback rewriting.

In M. Nivat, editor, Proc. Foundations of Software Science and

Computation Structures, volume 1378 of LNCS, pages 189{202.

Springer, 1998. 2.2

[Kle99] Renate Klempien-Hinrichs. The generative power of context-free node

rewriting in hypergraphs. Grammars, 2:211{221, 1999. 2.3

[Kle00] Renate Klempien-Hinrichs. Context-free Hypergraph Grammars. Node

and Hyperedge Rewriting with an Application to Petri Nets. PhD thesis,

Universit�at Bremen, 2000. 2.3

[Kle01] Renate Klempien-Hinrichs. Normal forms for context-free node-

rewriting hypergraph grammars. Math. Struct. in Comput. Sci., 2001.

To appear. 2.3

[Kle02] Renate Klempien-Hinrichs. Context-free hypergraph grammars with

node rewriting. In Bauderon and Corradini [BC02]. This volume. 2.3

[KM01] B. K�onig and U. Montanari. Observational Equivalence for

Synchronized Graph Rewriting. In Proceedings TACS'01, LNCS.

Springer, 2001. To appear. 5.1

[KMP00] M. Koch, L.V. Mancini, and F. Parisi Presicce. A Formal Model

for Role-Based Access Control using Graph Transformation. In

F. Cuppens, Y. Deswarte, D. Gollmann, and M. Waidner, editors, Proc.

of the 6th European Symposium on Research in Computer Security

(ESORICS 2000), number 1895 in LNCS, pages 122{139. Springer,

2000. 6.6

[KMP01a] M. Koch, L.V. Mancini, and F. Parisi Presicce. Foundations for a

graph-based approach to the Speci�cation of Access Control Policies.

In F. Honsell and M. Miculan, editors, Proc. of Foundations of Software

Science and Computation Structures (FoSSaCS 2001), LNCS. Springer,

2001. 6.6

[KMP01b] M. Koch, L.V. Mancini, and F. Parisi Presicce. On the Speci�cation

and Evolution of Access Control Policies. In S. Osborne, editor, Proc.

6th ACM Symp. on Access Control Models and Technologies, pages 121{

130. ACM, 2001. 6.6

[Koc97] Manuel Koch. Bedingte verteilte Graphtransformation und ihre

Anwendung auf verteilte Transaktionen. Technical Report 97-11,

Technical University of Berlin, 1997. 4.1

59

Corradini

[Koc99] Manuel Koch. Integration of Graph Transformation and Temporal

Logic for the Speci�cation of Distributed Systems. PhD thesis,

Technische Universit�at Berlin, FB 13, 1999. 3.4, 4.1

[Kus00] Sabine Kuske. Transformation Units { A Structuring Principle for

Graph Transformation Systems. PhD thesis, Universit�at Bremen, 2000.

4.4

[Kus01] Sabine Kuske. A formal semantics of UML state machines based

of structured graph transformation. In Proc. Fourth International

Conference on the Uni�ed Modelling Language, 2001. To appear. 4.4

[Kus02] Sabine Kuske. Parameterized transformation units. In Bauderon and

Corradini [BC02]. This volume. 4.4

[KV00] H.-J. Kreowski and G. Valiente. Redundancy and Subsumption in

High-Level Replacement Systems. In Ehrig et al. [EEKR00], pages

215{227. 2.4

[Lap98] Denis Lapoire. Recognizability equals monadic second-order

de�nability, for sets of graphs of bounded tree-width. In Proc. STACS

'98, volume 1373 of LNCS, pages 618{628, 1998. 3.3

[LMS99] I. Litovsky, Y. M�etivier, and E. Sopena. Graph relabelling systems and

distributed algorithms. In Ehrig et al. [EKMR99], chapter 1. 7, 8

[LR00] M. Llabres and F. Rossell�o. Pushout complements for arbitrary partial

algebras. In Ehrig et al. [EEKR00], pages 131{144. 2.5

[LV00] J. Larrosa and G. Valiente. Graph pattern matching using constraint

satisfaction. In Proc. Joint APPLIGRAPH and GETGRATS

Workshop on Graph Transformation Systems, pages 189{196, Berlin,

Germany, 2000. 6.8

[Man98] Sebastian Maneth. Cooperating distributed hyperedge replacement

grammars. In A. Kelemenov�a, editor, Proc. MFCS'98 Satellite

Workshop on Grammar Systems, pages 149{164, 1998. 2.3

[Man99] Sebastian Maneth. String languages generated by total deterministic

macro tree transducers. In W. Thomas, editor, Foundations of Software

Science and Computation Structures (FoSSaCS'99), volume 1578 of

LNCS, pages 258{272. Springer, 1999. 2.6

[MM97] Y. M�etivier and A. Muscholl. About the local detection of

termination of local computations. In The 4th International colloquium

on structural information and communication complexity. Carleton

University Press, 1997. 7

[MN99] S. Maneth and F. Neven. Recursive structured document

transformations. In Proceedings DBPL'99, 1999. 2.6

60

Corradini

[MPR99] U. Montanari, M. Pistore, and F. Rossi. Modeling concurrent, mobile

and coordinated systems via graph transformations. In Ehrig et al.

[EKMR99], chapter 4. 8

[MR98] U. Montanari and F. Rossi. Modeling process coordination via tiles,

graphs and constraints. In Proc. 3rd Biennial World Conference on

Integrated Design and Process Technology, volume 4, pages 1{8, 1998.

5.3

[MR99] U. Montanari and F. Rossi. Graph rewriting, constraint solving and

tiles for coordinating distributed systems. Math. Struct. in Comput.

Sci., 7(4):333{370, 1999. 4.1, 5.3

[MS97a] Y. M�etivier and E. Sopena. Graph relabelling systems: a general

overview. Computers and arti�cial intelligence, 16:167{185, 1997. 7, 8

[MS97b] M. Mosbah and N. Saheb. Formal rational fractions and random walks

on cycle graphs. In Proceedings 9th Conference on Formal Power Series

and Algebraic Combinatorics, 1997. Also: Technical Report 1147{96,

University of Bordeaux; To appear in Discrete Mathematics. 7

[MS97c] M. Mosbah and N. Saheb. A syntactic approach to random walks on

graphs. In 23rd International Workshop, WG'97, LNCS. Springer, June

1997. Also: Technical Report 1163{97, University of Bordeaux. 7

[MS99] M. Mosbah and N. Saheb. Non uniform random spanning trees on

weighted graphs. Theoret. Comput. Sci., 218, 1999. 7

[MSZ00] Y. M�etivier, N. Saheb, and A. Zemmari. Randomized rendezvous. In

Colloquium on mathematics and computer science: Algorithms, trees,

combinatorics and probabilities, Trends in mathematics. Birkhauser,

2000. 7

[MSZ01a] Y. M�etivier, N. Saheb, and A. Zemmari. A death process model

for randomized elections in trees. In Proc. GASCOM'01, Certosa di

Pontignano, 2001. 7

[MSZ01b] Y. M�etivier, N. Saheb, and A. Zemmari. Randomized local elections.

To appear, 2001. 7

[MT00a] Y. M�etivier and G. Tel. Termination detection and universal graph

reconstruction. In Proc. 7th International colloquium on structural

information and communication complexity, pages 237{251. Carleton

Scienti�c, 2000. 7

[MT00b] Y. M�etivier and G. Tel. Termination detection and universal graph

reconstruction. In Proceedings 7th International Colloquium on

Structural Information and Communication Complexity, pages 237{

251. Carleton Scienti�c, 2000. 7

[MV98] S. Maneth and H. Vogler. Attributed context-free hypergraph

grammars. J. Autom. Lang. Comb., 3(2):105{147, 1998. 2.3

61

Corradini

[NSM00] M. Nagl, A. Sch�urr, and M. M�unch, editors. Proceedings of Workshop

on Applications of Graph Transformation with Industrial Relevance

(AGTIVE'99), Kerkade, The Netherlands, September 1999, volume

1779 of LNCS, 2000. 8

[Pad99] Julia Padberg. Categorical Approach to Horizontal Structuring and

Re�nement of High-Level Replacement Systems. Applied Categorical

Structures, 7:371{403, 1999. 2.4

[Pel97] L. Pelecq. Isomorphismes et automorphismes des graphes contextfr-

free, �equationnels et automatiques. PhD thesis, Universit�e de Bordeaux

1, 1997. 2.10

[PER01] D.M. Prescott, A. Ehrenfeucht, and G. Rozenberg. Molecular

operations for DNA processing in hypotrichous ciliates. European

Journal of Protistology, 2001. To appear. 6.2

[PG98] J. Padberg and M. Gajewsky. Using High-Level Replacement Systems

to Preserve Safety Properties in Place/Transition Net Transformations.

In Engels and Rozenberg [ER98], pages 356{365. 2.4

[PGE98] J. Padberg, M. Gajewsky, and C. Ermel. Rule-Based Re�nement

of High-Level Nets Preserving Safety Properties. In E. Astesiano,

editor, Fundamental approaches to Software Engineering, volume 1382

of LNCS, pages 221{238. Springer, 1998. 2.4

[Plu97] Detlef Plump. Simpli�cation orders for term graph rewriting. In

I. Pr��vera and P. Ru�zi�cka, editors, Proc. Mathematical Foundations

of Computer Science 1997, volume 1295 of LNCS, pages 458{467.

Springer, 1997. 6.1

[Plu98] Detlef Plump. Termination of graph rewriting is undecidable.

Fundamenta Informaticae, 33(2):201{209, 1998. 2.1

[Plu99a] Detlef Plump. Computing by Graph Rewriting. Habilitation thesis,

Universit�at Bremen, Fachbereich Mathematik und Informatik, 1999.

6.1

[Plu99b] Detlef Plump. Term graph rewriting. In Ehrig et al. [EEKR99],

chapter 1, pages 3{62. 6.1, 8

[Plu02] Detlef Plump. Essentials of term graph rewriting. In Bauderon and

Corradini [BC02]. This volume. 6.1

[Roz97] Grzegorz Rozenberg, editor. Handbook of Graph Grammars and

Computing by Graph Transformation. Vol. 1: Foundations. World

Scienti�c, 1997. 8

[S�en97] G. S�enizergues. �(A) � �(B)? Technical Report nr1183-97, LaBRI,

Universit�e Bordeaux I, 1997. 2.8

62

Corradini

[S�en98a] G. S�enizergues. Decidability of bisimulation equivalence for equational

graphs of �nite out-degree. In Proceedings FOCS'98, pages 120{129.

IEEE Computer Society Press, 1998. 2.8

[S�en98b] G. S�enizergues. L(A) = L(B)? Technical report, LaBRI, Universit�e

Bordeaux I, 1998. Corrected and extended version of report 1161-97.

2.8

[S�en98c] G. S�enizergues. The equivalence problem for deterministic pushdown

transducers into abelian groups. In Proceedings MFCS'98, volume 1450

of LNCS, pages 305{315. Springer, 1998. 2.8

[S�en99] G. S�enizergues. T(A) = T(B)? In Proceedings ICALP'99, volume 1644

of LNCS, pages 665{675. Springer, 1999. 2.8

[Sim00] Marta Simeoni. A Categorical Approach to Modularization of Graph

Transformation Systems using Re�nements. PhD thesis, Dipartimento

di Informatica, Universit�a di Roma "La Sapienza", 2000. 4.5, 5.2

[Tae96] Gabriele Taentzer. Parallel and Distributed Graph Transformation:

Formal Description and Application to Communication-Based Systems.

PhD thesis, TU Berlin, 1996. Shaker Verlag. 4.1

[Tae97] Gabriele Taentzer. Parallel High-Level Replacement Systems. Theoret.

Comput. Sci., 186, November 1997. 2.4

[Tae99] Gabriele Taentzer. Distributed Graphs and Graph Transformation.

Applied Categorical Structures, 7:431{462, 1999. 4.1

[Tae02] Gabriele Taentzer. Visual Modeling of Distributed Object Systems

by Graph Transformation. In Bauderon and Corradini [BC02]. This

volume. 4.1

[TE00] G. Taentzer and H. Ehrig. Semantics of distributed system

speci�cations based on graph transformation. Technical Report 0005,

LMU M�unchen, Institut f�ur Informatik, September 2000. 4.1

[TGM99] G. Taentzer, M. Goedicke, and T. Meyer. Dynamic accomodation of

change: Automated architecture con�guration of distributed systems.

In Proceedings Automated Software Engineering'99. IEEE Computer

Society, 1999. 4.1

[TGM00] G. Taentzer, M. Goedicke, and T. Meyer. Dynamic change management

by distributed graph transformation: Towards con�gurable distributed

systems. In Ehrig et al. [EEKR00], pages 179{193. 4.1

[tHBG99] P.J. 't Hoen, G. Busatto, and L. Groenewegen. Instance level packages

for UML. Technical Report 99-06, Leiden Institute of Advanced

Computer Science, Vakgroep Informatica, Leiden, NL, 1999. 4.4

[TK97] G. Taentzer and M. Koch. Distributing attributed graph

transformation. In First European Workshop on \General Theory of

Graph Transformation Systems", Bordeaux, Oct. 8-10,1997, 1997. 4.1

63

Corradini

[VM97] G. Valiente and C. Mart��nez. An algorithm for graph pattern-matching.

In Proc. 4th South American Workshop on String Processing, volume 8

of International Informatics Series, pages 180{197. Carleton University

Press, 1997. 6.8

[Wol98] Dietmar Wolz. Colimit Library for Graph Transformations and

Algebraic Development Techniques. PhD thesis, Technical University

of Berlin, Dep. of Comp. Sci., 1998. 4.6

64