Towards a General Approach for Symbolic Model-Checker Prototyping

Towards a General
Approach for Symbolic
Model-Checker Prototyping
Edmundo López Bóbeda, Maximilien Colange, Didier Buchs
Wednesday, September 24th 2014 - Enschede, Netherlands
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Your awesome DSL
Abstract semantics
2

Your awesome DSL
Abstract semantics
Symbolic
Model checker
2

Your awesome DSL
Abstract semantics
3

Your awesome DSL
Abstract semantics
Existing Symbolic
Model checker
3

Your awesome DSL
Abstract semantics
Translation
Existing Symbolic
Model checker
3

Your awesome DSL
Abstract semantics
Translation
Existing Symbolic
Model checker
4

Your awesome DSL
Translation
Existing Symbolic
Model checker
4

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation
high level data structures

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation
custom operations

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation
custom operations
rich data types

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation
custom operations
rich data types
low level

Your awesome DSL
Existing Symbolic
Model checker
4
}Too much
work!
Translation
custom operations
rich data types
low level
fixed primitives operations

Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams
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Your awesome DSL
Abstract semantics
approach
{Our Translation Translation
Set rewriting
Decision diagrams
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Your awesome DSL
Abstract semantics
approach
{Our Translation Translation
Set rewriting
Decision diagrams
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}Our contribution

Abstract semantics
In context
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Abstract semantics
In context
• High level representation
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Abstract semantics
In context
• High level representation
• Suitable for humans
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Abstract semantics
Variable assignation
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s
hB := c, si ! s[B = k/B = c]

Abstract semantics
• Let s be a state of a system
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s
hB := c, si ! s[B = k/B = c]

Abstract semantics
• s = {A = k1, B = k2, …}
7
s
hB := c, si ! s[B = k/B = c]

Abstract semantics
• s = {A = k1, B = k2, …}
• k, k1, k2, c ∈ 퓝
7
s
hB := c, si ! s[B = k/B = c]

Abstract semantics
• s = {A = k1, B = k2, …}
• k, k1, k2, c ∈ 퓝
• A, B, etc variable names
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s
hB := c, si ! s[B = k/B = c]

Set rewriting
In context
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Set rewriting
In context
• Rewriting and strategies
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Set rewriting
In context
• Good semantic framework
[Martí-Oliet & Meseguer 1993]
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Set rewriting
In context
• Good semantic framework
[Martí-Oliet & Meseguer 1993]
• Operational semantics
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

Set rewriting
A state
• Variables
• var(A, 0, var(B, 2, var(C, 3, empty)))
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Set rewriting
Operational semantics / Variable Assignation
s
hB := c, si ! s[B = k/B = c]
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• var(B, $x, $s) ⤳ var(B, c, $s), k ∈ 퓝
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• var(B, $x, $s) ⤳ var(B, c, $s), k ∈ 퓝
• Problem:
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• var(B, $x, $s) ⤳ var(B, c, $s), k ∈ 퓝
• Problem:
• Non determinism ⇒ performance hit, ambiguity
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Rewriting strategies
Goal
• Introduced in ELAN [Borovanský et al.1996]
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Goal
• Control rewriting
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Goal
• Avoid ambiguity
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Goal
• Avoid ambiguity
• Improve speed
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What are they
Rewrite
rules
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What are they
Strategies
Rewrite
rules
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Basic strategy
• Basic strategy (A list of rewrite rules)
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Basic strategy
• Application to root term only
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Basic strategy
• The first applicable rule is applied
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Basic strategy
• The first applicable rule is applied
• Otherwise, fail
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Other useful strategies
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• Identity[t] = t
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• Identity[t] = t
• Fail[t], always fails
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• Identity[t] = t
• (S1 orElse S2)[t] = S1[t], or S2[t] if S1[t] fails
• Conditional application of strategies
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• Identity[t] = t
• (S1 andThen S2)[t] = S2[S1[t]]
• Sequential composition of strategies
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• Identity[t] = t
• (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
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• assignK = { var(B, $x, $s) ⤳ var(B, c, $s) }
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• applyToB(S) = S orElse (Subterm3(applyToB(S)))
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
• applyToB(S) = S orElse (Subterm3(applyToB(S)))
• transition = applyToB(assignK)
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Set rewriting
s
hB := c, si ! s[B = k/B = c]
assignK = { var(B, $x, $s) ⤳ var(B, c, $s) }
applyToB(S) = S orElse (Subterm3(applyToB(S)))
transition = applyToB(assignK)
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Set rewriting
Set extension
• In practice
• Strategies and rewrite rules applied to sets of
terms
• Allow also to describe model checking
computation
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Set rewriting
Set extension
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Set rewriting
Set extension
• Natural extension
• S[{t1, …, tn}] = {S[t1], …, S[tn]}
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Set rewriting
Set extension
• Natural extension
• S[{t1, …, tn}] = {S[t1], …, S[tn]}
• Set strategies, T = {t1, …, tn}
• Union(S1, S2)[T] = S1[T] U S2[T], if both
succeed
• Fixpoint(S)[T] = μT.S[T]
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Set rewriting
Computing state space
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Set rewriting
19
s
hB := c, si ! s[B = k/B = c]
transition1 = …

Set rewriting
19
s
hB := c, si ! s[B = k/B = c]
transition1 = …
semantic formula 2 transition2 = …

Set rewriting
19
s
hB := c, si ! s[B = k/B = c]
transition1 = …
…

Set rewriting
19
s
hB := c, si ! s[B = k/B = c]
transition1 = …
…
semantic formula n transitionn = …

Set rewriting
19
s
hB := c, si ! s[B = k/B = c]
transition1 = …
…
semantic formula n transitionn = …
calculateSS = Fixpoint(Union(transition1, transition2, …, transitionn))

Set rewriting
Saturation: For connaisseurs
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Set rewriting
• Well known DD optimization technique
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Set rewriting
• Apply local fixpoint in order to reduce peak effect
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Set rewriting
• Satn(S) =
(Subtermn(Satn(S)) orElse FixPoint(S)) andThen Fixpoint(S)
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Set rewriting
• Satn(S) =
(Subtermn(Satn(S)) orElse FixPoint(S)) andThen Fixpoint(S)
var(A, 1, var(B, 2, var(C, 0, empty )))
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Decision Diagrams
In context
• Fast
• Large state spaces
• Suitable for model checking
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Your awesome DSL
Abstract semantics
Translation
Set rewriting
Translation
Decision diagrams

The idea is that you never have
to think in terms of DD again…
so we won’t talk about them :-)
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Implementation
• We have a tool that implements the approach
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Implementation
• Stratagem http://sourceforge.net/projects/stratagem-mc/
(written in Java and Scala)
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Implementation
• ~3700 lines of Scala code (DD and Strategies engine)
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Implementation
• Java code generated from model (Eclipse EMF, XText)
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Implementation
• Implemented translation for Petri nets
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Implementation
• Implemented translation for Petri nets
• Implemented translation for SPIN-like formalism
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Practical results
Presentation
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Practical results
Presentation
• Petri nets taken from the Model checking contest @
PETRI NETS 2014 [Kordon et al. 2014]
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Practical results
Presentation
• Marcie [Heiner et al. 2013] was the best model
checker for the state space category
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Practical results
Presentation
• Marcie [Heiner et al. 2013] was the best model
checker for the state space category
• Since then we only improved the translation
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Practical results
Kanban problem
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Practical results
Kanban problem
• Small Petri net
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Practical results
Kanban problem
• Small Petri net
• 16 places & 16 transitions, marking changes with
scale parameter
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Practical results
Kanban problem
• Small Petri net
scale parameter
• State space for scale parameter 100
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Practical results
Kanban problem
• Small Petri net
scale parameter
• 1.7263 ·1019 states
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Practical results
Kanban problem
Marcie Stratagem
10 20 50 100
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100
Time in seconds 0.1
10
1
Model size (scale parameter)

Practical results
Sharedmem problem
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Practical results
Sharedmem problem
• Petri net’s places and transition increase with scale
parameter
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Practical results
Sharedmem problem
parameter
• 2651 places & 5050 transitions for scale parameter
50
27

Practical results
Sharedmem problem
parameter
50
27

Practical results
Sharedmem problem
parameter
50
• 5.87 ·1026 states
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Practical results
SharedMem problem
Marcie Stratagem
5 10 20 50
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Time in seconds
1000
100
10
1
0.1
Model size (scale parameter)

Limitations
• Non-linear rules are not allowed (but can be
simulated)
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Limitations
• Non-linear rules are not allowed (but can be
simulated)
• Verification not yet implemented
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Conclusions
• New approach
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Conclusions
• New approach
• Better results just by changing the strategy
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Conclusions
• New approach
• More general and unified
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Conclusions
• New approach
• More general and unified
• Good benchmarks
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Future work
• Systematically go from SOS rules to rewrite
strategies
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Future work
strategies
• Create more translations
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Future work
strategies
• Create more translations
• Implement CTL model checking using strategies
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Bibliography
!
Narciso Martí-Oliet and José Meseguer. Rewriting Logic as a Logical and
Semantic Framework.1993
Peter Borovanský and Claude Kirchner and Hélène Kirchner and Pierre-
Etienne Moreau and Marian Vittek. ELAN: A logical framework based on
computational systems. Electronic Notes in Theoretical Computer
Science 4(0):35 – 50, 1996.
M Heiner, C Rohr and M Schwarick. MARCIE - Model checking And
Reachability analysis done effiCIEntly; In Proc. PETRI NETS 2013, Milano,
Springer, LNCS, volume 7927, pages 389–399, June 2013
Kordon et al. HTML results from the Model Checking Contest @ Petri Net
(2014 edition). http://mcc.lip6.fr/2014, 2014
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The paper for this presentation can
be found at: http://
edmundo.lopezbobeda.net/
publications
34

Towards a General Approach for Symbolic Model-Checker Prototyping

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