Building Verifiable Software Prototypes Using Coloured Petri NetsQualifying Exam 1/39 June 17, 2005...

June 17, 2005

Building Verifiable Software Prototypes Using Coloured Petri Nets Qualifying Exam

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Building VerifiableSoftware Prototypes

Using Coloured Petri Nets

Michael WestergaardDepartment of Computer Science

University of AarhusDenmark

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Overview

• Example• Towards a New State-space Tool• Model-based Prototyping and Animation• Towards an Interchange Format for

Coloured Petri Nets

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Example (1/2)

• 2 runners in a race, halfway throughthe race is a stand with water

• Either run) a runner runs to the drink stand,win) a runner wins the race, orlose) a runner loses the race

• Only one runner can win the race• In the beginning neither of the runners

have finished any laps

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Example (2/2)

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Example (2/2)

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Example (2/2)

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Example (2/2)

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Example (2/2)

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Towards a New State-space Tool

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Analysis

• We want to check that our model contains no errors (e.g. that at most one runner can win)

• Generate the state space, a directed graph with states as nodes and transitions as edges

• The problem: The state space is large• Solution: Make the state space smaller,

store only parts of it, or represent the state space in a clever way

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The Sweep-Line Method• We assume a progress

measure, , that assigns to each state a progress value, such thats->s’ => (s)≤ (s’)

• Here, we take (n,m,b)=n

• All states to be processed are in front of the sweep-line

• All new states are added in front of the sweep-line

• We do not need the states behind the sweep-line; they can safely be removed from memory progress

0 1 32

Not yet discovered state

Discovered but unprocessed state

Processed state

sweep-line

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A CondensedRepresentation

• We want to represent the entire state space• A state of the system is (n,m,b) with

n,m{0…3} and b {u,d}• Only some (10) of the syntactically possible states

(4·4·2=32) are reachable• At least ceil(log(32))=5 bits are used to store each

state, although ceil(log(10))=4 bits would suffice• In realistic examples, the number of syntactically

possible states is much larger than the number of reachable states, so distinguishing only between reachable states yields a good reduction

• Alas, we first know the number of reachable states, when we have constructed the reachability graph

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Neighbor List• We assume that we can

enumerate the transitions

• Assign to each reachable state a number, 0…R-1

•

Number of transitions

Transition

Destination state

State number

0

1

0

2

0

0

1

11

11

2

0 1

2 3

54

6

9

8

7

0 = run

1 = win

2 = lose

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On-the-fly Construction of the Condensed Representation

State number

Number of transitions

New header:

Number of bits used to represent the successor states

Transition

Destination state

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Experimental Results

• In the report, I present an architecture of a state-space tool

• A prototypical implementation of the described method has been made in the state-space tool presented in the report

• The implementation does not take into account the different sizes of the numbers, and encodes everything in a machine word

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Experimental Results(Database Managers)

0.0

2.5

5.0

7.5

10.0

12.5

3 4 5 6 7 8 9 10

size/mb

Database Managers

0.00

0.50

1.00

1.50

2.00

2.50ratio

Full sizeCondensed sizeSize ratioTime ratio

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Experimental Results(Dining Philosophers)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20

size/mb

Philosophers

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0ratio

Full sizeCondensed sizeSize ratioTime ratio

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Model-based Prototyping and Animation

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Need for Visualization

• While the modeling language is graphical, the model is difficult to grasp unless you know Coloured Petri nets or some similar formalism

• It would be nicer to see the model like this:

• The goal of this work is to make this possible

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Model-driven Prototype Approach

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Model-View-Controller

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Model-View-Controller

Animation GUICPN model

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Architecture

View ViewController +

Model

AnimationPrototype

GUI

Model-driven prototypePrototype

GUI

Final product

Real

implementation

Test

driver

Verification

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Case-study: Interoperability Protocol

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Towards an Interchange Format for Coloured Petri Nets

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Benefits of being Able to Interchange Coloured Petri Nets

• Repository of models– Teaching– Benchmarks

• It is possible to build tools are able to construct models and other tools that analyze the models

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Difficulties

• Labels are not just non-negativeintegers, but can range over anarbitrary domain – is “1`r(1)++1`r(2)”the same as “<r(1)>+1*<r(2)>”?

• High-level Petri nets (HLPN) often support elaborate composition mechanisms, which have to be dealt with – should we extend PNML to support hierarchical nets? (See the report)

Start

1`r(1)++1`r(2)

RUNNER

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Start

1`r(1)++1`r(2)

RUNNER

• Take as example a net witha place named Start withdomain RUNNER andinitial marking one tokenwith value r(1) and onetoken with value r(2)

• We notice1) Three labels, the domain, the initial marking, and

the name2) The initial marking is rather complex, and several

reasonable concrete syntaxes can express it, e.g.• CPN Tools: 1`r(1)++1`r(2)• CPN-AMI: <r(1)> + 1*<r(2)>

Labels

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Example• We would store the initial marking as follows

(using the concrete syntax of CPN Tools):<initialMarking> <text>1`r(1)++1`r(2)</text></initialMarking>

Advantage• Very simple approach; easy to implement and

understand

Disadvantage• Different tools use different syntaxes to express the

same– CPN Tools: 1`r(1)++1`r(2), or– CPN-AMI: <r(1)> + 1*<r(2)>.and this makes interchange difficult

Start

1`r(1)++1`r(2)

RUNNER

Labels – Solution 1:Store as Concrete Syntax

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Labels – Solution 2:Store as Abstract Syntax Tree

Example• We would store the initial marking as follows:

<initialMarking> <multiset> <value cardinality=”1”><text>r(1)</text></value> <value cardinality=”1”><text>r(2)</text></value> </multiset></initialMarking>

Advantage• Eliminates differences in concrete syntax

Disadvantages• Difficult to make simple editors that do not completely

parse and check inscriptions• Cumbersome to add new features, as a new AST node has

to be defined

Start

1`r(1)++1`r(2)

RUNNER

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Labels – Solution 3:Mix Abstract and Concrete Syntax

Example• We would allowing the initial marking to be

stored as either:<initialMarking> <text>1`r(1)++1`r(2)</text></initialMarking>

or<initialMarking> <multiset> <value cardinality=”1”><text>r(1)</text></value> <value cardinality=”1”><text>r(2)</text></value> </multiset></initialMarking>

Advantages• Tools can save as much or as little using abstract syntax

as desired – trade-off between interchangeability and simplicity

• New features can easily be incorporated by using concrete syntax until an appropriate AST node is defined

Start

1`r(1)++1`r(2)

RUNNER

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Added benefits• Allows an incremental transition to the

interchange format, as tool implementers can choose to save only some (parts of) labels as ASTs

• Allows the format to be used as primary storageformat, as incorrect (and therefore unparsable) inscriptions can be saved using concrete syntax

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Conclusion and Future Plans

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ConclusionState-space Analysis

• We have seen an efficient representation of reachability graphs, and how this representation can be traversed for analysis

• We have seen how the efficient representation can be calculated efficiently using the sweep-line method

• We have seen how the method performs on some examples – basically, the method performs well when the sweep-line method performs well, i.e. for systems with a clear notion of progress

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ConclusionModel-based Prototyping

• We have seen that animation of formal models may be beneficial

• We have introduced the architecture of a tool to support animation of formal models

• The architecture is based on the Model-View-Controller design pattern

• By interchanging parts, the animation tool supports– Animation of models– Model-based prototyping– The final product– Verification

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ConclusionInterchange Format

• We have shown 3 different ways to represent labels:1) using concrete syntax only,2) using abstract syntax only, and3) using a mixture of concrete and abstract syntax.

• We have argued that the 3rd way is the best, as it is more flexible and allows interchange between tools not sharing concrete syntax

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Main ContributionsState-space• Design/implementation of new state-space tool• Design/implementation/test of new reduction

technique• Design/implementation of state-space analysis of

Bigraphical Reactive SystemsModel-based prototyping/animation• Design/implementation of animation tool

– Very flexible architecture

• Use of animation tool in case-studyInterchange of Coloured Petri nets• Mix of concrete and abstract syntax for labels• Translations from common composition mechanisms

to Modular PNML

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Future Work

• Work on model-based prototyping and interchanging Coloured Petri nets is done

• I will concentrate on state-space analysis during part B– Benchmark the sweep-line method– Visit to Aalborg– Modal logic for (Coloured) Petri nets– Partial state spaces– Telebit project– ...

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Not a clear-cut separation• E. Kindler proposes in the April 2004

proposal for ISO/IEC 15909-2 a similarapproach to the representation labels

• Kindlers proposal requires that a label is stored either using concrete syntax or using abstract syntax

• Our proposal allows <initialMarking> <multiset> <value cardinality=”1”><text>r(1)</text></value> <value cardinality=”1”><text>r(1+1)</text></value> </multiset></initialMarking> which clearly is a multi set even if function application is not standardized

• Thus not having a clear-cut separation of abstract and concrete syntax makes it easy to simulate new AST nodes

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Composition Constructs• A number of composition constructs

exist for high-level Petri nets:– Hierarchical nets– Fusion places– Synchronous channels– etc.

• Composition mechanisms can be represented by adding new labels or special nodes– Example: Fusion places can be implemented by

adding a label fusionGroup, which indicates to what fusion group the place belongs

• In the report, I present a translation to Modular PNML

Building Verifiable Software Prototypes Using Coloured Petri NetsQualifying Exam 1/39 June 17, 2005...

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