TMPA-2017: Compositional Process Model Synthesis based on Interface Patterns

Compositional Process Model Synthesis based onInterface Patterns

TMPA-2017

Roman A. Nesterov Irina A. [email protected], [email protected]

Laboratory of Process-Aware Information SystemsNational Research University

Higher School of Economics (Moscow)

March 3, 2017

[email protected]

[email protected]

Agenda

1. Introduction2. Preliminaries

• Petri nets and their properties

3. Related Work4. Composing Petri nets via interfaces

• General description• Composition patterns

5. Conclusion

R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 2 / 25

Introduction

Problem• Distributed systems with several interacting components –

large-scale models• Coordination and verification problems – too many possible

states to check

Approach• Study a system compositionally – a system inherits

component properties• Composition patterns for constructing system models – a

library of patterns to obtain correct system models


Petri netsStructure

A B

B

B

A Petri net is a bipartite graph N = (P,T,F,m0,L), where:1. P = {p1, p2, p3, ..., pn}2. T = {t1, t2, t3, ..., tm}, P ∩ T = ∅3. F ⊆ (P × T) ∪ (T × P)4. m0 ⊆ P5. L : T → {A, τ}

•t = {p ∈ P|(p, t) ∈ F}, t• = {p ∈ P|(t, p) ∈ F}, •t• = •t ∪ t•


Petri netsBehavior and correctness

A B

B

B

A occurred

1. A transition is enabled at m iff •t ∈ m and m ∩ t• = ∅2. A marking m is final iff ∀p ∈ m : p• = ∅3. A marking m is dead iff it enables no transitions (deadlock),

except for a final one4. A net N is correct iff:

• There are no deadlocks• A final marking is reachable


Related workComposing Petri nets by merging places, transitions [Reisig, 2013]

D

E

C

p

A

B p

D

E

CA

B p

N1

N2 Composition

• Straightforward way to compose nets• Correctness of a composed net?


Related workComposing Petri nets by net morphisms [Pomello et al., 2007-1014]

C D

A

B

A

B

E F

A1A

B

E F

A

C D

B

N1

N2 Composition

• Interacting nets are refinements of an abstract system modelR. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 7 / 25

Related workAlgebra of web services [Hamadi et al., 2003]

S1

S2

S1S

2

S1

S2

Sequencing Choice Concurrency

Correct

services

• Web services are correct Petri nets• Input-output relations between interacting services


Motivating exampleCausality on inner actions of interacting Petri nets

…

B

…

…

A

…

A

B

Components

Interface

A correct

Petri net

• Two components• Observable actions A, B• Correct behavior

ProblemHow to compose nets to get:

• correct composition;• property inheritance;• concurrency preservation?

SolutionTo adjust approach based onmorphisms to this case


MorphismsDefinition

Let Ni = (Pi,Ti,Fi,mi0) for i = 1, 2 be two Petri nets,

Xi = Pi ∪ Ti. The ω-morphism is a map φ : X1 → X2 such that:1. φ(P1) = P2, φ(m1

0) = m20.

2. ∀t1 ∈ T1 : φ(t1) ∈ T2 ⇒ φ(•t1) = •φ(t1) andφ(t1•) = φ(t1)•.

3. ∀t1 ∈ T1 : φ(t1) ∈ P2 ⇒ φ(•t1•) = {φ(t1)}.

A

A’ A

B

B’


Composing Petri nets via morphismsStep 1. Constructing canonical representations

NC is a canonical representation with respect to an interface

A

A B

A A B

B

A

A B

A

A BB

N Interface NC


Composing Petri nets via morphismsStep 2. Defining morphisms and merging nets

C D

A

B

A

B

E F

A1A

B

E F

A

C D

B

N1

N2 Composition


Composing Petri nets via morphismsPreservation of properties

How properties are preserved?Let N1 and N2 be two Petri nets representing components, and Nbe their composition obtained via the interface Petri net NI andω-morphisms as described above.

1. The Petri net N is deadlock-free, if N1, N2 and NI aredeadlock-free.

2. The Petri net N terminates properly, if N1, N2 and NIterminates properly.

A composed net is correct iff component nets are correct


Compositional patternsGeneral idea

Compositional pattern is a ready-to-use instrument for modellingand studying distributed systems with several interactingcomponents:

• Patterns are developed for typical workflows• Pattern correctness is justified via net morphism usage• Pattens can be applied without theoretical knowledge


Pattern 1: Simple causalityProblem statement

…

B

…

…

A

…

A

B

Components

Interface

A

B

Extended interface

Termination

Start

A correct

Petri net

• Extended interface is weakly bisimilar to the original one• Preservation of concurrency


Pattern 1: Simple causalityPrimary composition result

N1(S1)

A

N1(S2)

B

N2(S1)

B

N2(S2)

A

A

B

N1(S1)

A

N2(S1)

B

N1(S2)

N2(S2)

Morphisms

Composition

N1

N2

To be

removed


Pattern 1: Simple causalityReduced composition result

N1(S1)

A

N1(S2)

B

N2(S1)

B

N2(S2)

A

A

B

N1(S1)

A

N2(S1)

B

N1(S2)

N2(S2)

Morphisms

Composition

N1

N2


Pattern 2: Extended causalityProblem statement

N1(S3)

A

N1(S4)

N1(S2)

N1(S1)

A

N2(S3)

B

N2(S4)

N2(S2)

N2(S1)

A

A

B

Components

Interface

A B

A A

Extended interface

N1

N2

Termination

Start


Pattern 2: Extended causalityComposition result and implications

N1(S3)

A

N1(S4)

N1(S2)

N1(S1)

A

N2(S3)

B

N2(S4)

N2(S2)

N2(S1)

A

Result• Introducing additional

controlling places• Clearly identified behavior

of components• Component properties are

inherited by construction


Pattern 3: Conditional causalityProblem statement

N1(S3)N1(S2)

N1(S1)

A B

N1(S5) N1(S4)

N2(S1)

C

N2(S2)

A

BC

C

Components

Interface

N1

N2

Problem2 copies of C will not allow to definemorphisms as surjective maps

SolutionReconstruction of the interface net


Pattern 3: Conditional causalityInterface modification

A C

A C

2

1

B

3

C

4

Construction idea1. Restrict execution of C2. Remember execution of A3. Restrict execution of B4. Forbid execution of B when

A occurs


Pattern 3: Conditional causalityComposition result and implications

N1(S1)

A A

N1(S2) N1(S3)N2(S1)

A BC

N2(S2)N1(S4)

C

N1(S5)

To sum up...Morphisms help organize connectionof inner actions of componentsimmediately by construction


Conclusion

• Compositional approach to modeling distributed systems• Component relations can be defined on inner actions• Patterns for composition (causality and its generalizations)

Future research directions• Coverage of over relations (e.g., choice)• Combination of patterns• Relations on several actions


References

1. Reisig, W.: Understanding Petri nets. Springer-Verlag BerlinHeidelberg (2013)

2. Bernardinello, L., Mangioni, E., Pomello, L.: Composition ofelementary net systems based on morphisms. CEUR WorkshopProceedings 853, 87–101 (2012)

3. Bernardinello, L., Monticelli, E., Pomello, L.: On PreservingStructural and Behavioural Properties by Composing Net Systemson Interfaces. Fundamenta Informaticae 80(1-3), 31–47 (2007)

4. Pomello, L., Rozenberg, G., Simone, C.: A survey of equivalencenotions for net based systems. Advances in Petri Nets 1992 pp.410–472 (1992)

5. Hamadi, R., Benatallah, B.: A Petri net-based model for webservice composition. Proceedings of the 14th Australasian DatabaseConference 17, 191–200 (2003)

6. Murata, T.: Petri Nets: Properties, Analysis and Applications.Proceedings of the IEEE 77(4), 541–580 (1989)


Thank you for your attention!

Compositional Process Model Synthesisbased on Interface PatternsRoman A. Nesterov Irina A. Lomazova

[email protected], [email protected]

Laboratory of Process-Aware Information SystemsNational Research University

Higher School of Economics (Moscow)

March 3, 2017


[email protected]

[email protected]

TMPA-2017: Compositional Process Model Synthesis based on Interface Patterns

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