StrataGEM: A Generic Petri Net

Verification FrameworkEdmundo López Bóbeda, Maximilien Colange, Didier Buchs

Wednesday, June 25th 2014 - Tunis, Tunisia

Petri nets 2014

Stratagem

Model checker

Photo: FastJack/Flickr" http://www.flickr.com/photos/fastjack/282707058/

Prototyping lab

Goal

Your formalism Your Model checker

Creating your model checker: A Checklist

• Semantics

• Description of the computation

• Optimizations

HowTerms

Strategies Rewrite rules

Semantics A running example

R

Y

G

t3t1

t2

R(suc(0), Y(0, G(0, empty)))

"

"

"

"

Representing a stateR

Y

G

t3t1

t2

Term = State

R(suc(0), Y(0, G(0, empty)))

iArc = R(suc(x), p) ↝ R(x, p)

oArc = G(x, p) ↝ G(suc(x), p)

"

"

Representing arcsR

Y

G

t3t1

t2Rewrite rules

Representing transitionsR

Y

G

t3t1

t2

R(suc(0), Y(0, G(0, empty)))

iArc = R(suc(x), p) ↝ R(x, p)

oArc = G(x, p) ↝ G(suc(x), p)

t1 = ???

"

Strategies in a nutshell

Strategies Rewrite rules

Terms

Strategies in a nutshell

Strategies

Rewrite rules

Basic strategy semantics

• Basic strategy (A list of rewrite rules)

• Application to root term only

• The first applicable rule is applied

• Otherwise, fail

Other useful strategies• Identity[t] = t

• Fail[t], always fails

• (S1 orElse S2)[t] = S1[t] or S2[t], if S1[t] fails

• Conditional application of strategies

• (S1 andThen S2)[t] = S2[S1[t]]

• Sequential composition of strategies

• Subtermk(S)[f(t1, …, tn)] = f(t1, …, S(tk), …, tn)

• Apply strategy to subterm

Representing transitionsR(suc(0), Y(0, G(0, empty)))

iArc = R(suc(x), p) ↝ R(x, p)

oArc = G(x, p) ↝ G(suc(x), p)

t1 = Once(iArc) andThen Once(oArc)

Once(S) = S orElse Subterm2(Once(S)

R

Y

G

t3t1

t2

Creating your model checker: A Checklist

• Semantics

• Description of the computation

• Optimizations

t1 = Once(iArc) andThen Once(oArc)

t2 = … ; t3 = …

CalcSS = ???

"

"

Description of the computation

R

Y

G

t3t1

t2

Strategies extended• Natural extension

• S[{t1, …, tn}] = {S[t1], …, S[tn]}

• Set strategies

• Union(S1, S2)[T] = S1[T] U S2[T], if both succeed

• Fixpoint(S)[T] = μT.S[T]

t1 = Once(iArc) andThen Once(oArc)

t2 = … ; t3 = …

CalcSS = Fixpoint(

Union(

Try(t1), Try(t2), Try(t3), Identity))

Try(S) = S orElse Identity

Description of the computation

R

Y

G

t3t1

t2

Creating your model checker: A Checklist

• Semantics

• Description of the computation

• Optimizations

Decision Diagram Operations

Trans. Trans.

State Space

Verification

Optim 1

Your formalism

Oth

er m

odel

che

cker

s

Decision Diagram Operations

Trans. Trans. Trans.

State Space

Verification

Optim 1

Optim 2

Your formalism

Oth

er m

odel

che

cker

s

Decision Diagram Operations

Trans. Trans. Trans.

State Space

Verification

Optim 1

Optim 2

Your formalism

Oth

er m

odel

che

cker

s

Engine

Decision Diagram Operations

Translation

Stra

tage

mSemantics, State Space,

OptimizationState

SpaceVerification Optim 1 Optim 2

Your formalism

=

Engine

Decision Diagram Operations

Translation

Stra

tage

mSemantics, State Space,

Optimization

Your formalism

Translation

Saturation: for connaisseurs• Well known DD optimization

technique

• Apply local fixpoint in order to reduce peak effect

R

Y

G

t3t1

t2Satn(S) = (Subtermn(Satn(S)) orElse FixPoint(S)) andThen Fixpoint(S)

Saturation: for connaisseursR

Y

G

t3t1

t2

Satn(S) = (Subtermn(Satn(S)) orElse FixPoint(S)) andThen Fixpoint(S)

R(1, Y(0, G(0, empty )))

Creating your model checker: A Checklist

• Semantics

• Description of the computation

• Optimizations

Practical results

• Stratagem has been used to implement:

• Optimizations: Saturation, Clustering, Anonymization, etc.

• Other formalisms: Divine formalism

Practical results• Comparison with PNXDD

• Symbolic model checking

• Similar techniques (topological, decision diagrams)

• Common model database (model checking contest)

• 2nd best tool for state space calculation last year

Practical resultsRa

tio ti

me

PNXD

D/ti

me

Stra

tage

m

0

0.35

0.7

1.05

1.4

Model size (scale parameter)

5 10 20 50 100 200

Erathostenes Railroad Shared Mem

Implementation

• 3700 lines of Scala

• Available for download http://sourceforge.net/projects/stratagem-mc/

• Source code available on Github

• Platform independent

Future work

• Implement CTL verification

• Implement other translations (Algebraic Petri nets)

• Implement other optimization techniques

Thank you! Any questions?

The paper for this presentation can be found at: http://

edmundo.lopezbobeda.net/publications