Property preserving abstractions for the verification of concurrent systems

Loiseaux, Claire; Graf, Susanne; Sifakis, Joseph; Bouajjani, Ahmed; Bensalem, Saddek

doi:10.1007/bf01384313

Cited by 281 publications

(167 citation statements)

References 25 publications

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“…Loiseaux, et al [22], proved that all P-properties true of an over-approximating transition relation are preserved in the corresponding concrete transition relation and that when one over-approximating transition relation is more precise than another, then the first preserves all the P-properties of the second. Dams extended this result to under-approximations and Q-properties and proved that his definitions of R best and R best possess the most PQ-propositions of any sound, mixed transition system.…”

Section: Validation and Refutation Logicsmentioning

confidence: 99%

“…In addition to Dams's work [10,11], three other lines of research deserve mention: Loiseaux, et al [22] showed an equivalence between simulations and Galois connections: For sets C and A, and ρ ⊆ C × A, they note that P(C) post[ρ],p re[ρ] P(A) is always a Galois connection. 18 For R ⊆ C × C and R ⊆ A × A, simulation is equivalently defined as R is ρ-simulated by R iff R −1 · ρ ⊆ ρ · (R ) −1 Treating R −1 and (R ) −1 as functions, we can define Galois-connection soundness as (R ) −1 is a sound over-approximation for R −1 with respect to γ iff…”

Section: Related Workmentioning

confidence: 99%

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Closed and Logical Relations for Over- and Under-Approximation of Powersets

Schmidt

2004

Static Analysis

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Abstract. We redevelop and extend Dams's results on over-and underapproximation with higher-order Galois connections: (1) We show how Galois connections are generated from U-GLB-L-LUBclosed binary relations, and we apply them to lower and upper powerset constructions, which are weaker forms of powerdomains appropriate for abstraction studies.(2) We use the powerset types within a family of logical relations, show when the logical relations preserve U-GLB-L-LUB-closure, and show that simulation is a logical relation. We use the logical relations to rebuild Dams's most-precise simulations, revealing the inner structure of overand under-approximation. (3) We extract validation and refutation logics from the logical relations, state their resemblance to Hennessey-Milner logic and description logic, and obtain easy proofs of soundness and best precision.Almost all Galois-connection-based static analyses are over-approximating: For Galois connection, (P(C), ⊆) α o , γ (A, A ), an abstract value a ∈ A proclaims a property of all the outputs of a program. For example, even ∈ Parity (see Figure 2 for the abstract domain Parity) asserts, "∀even" -all the program's outputs are even numbers, that is, the output is a set from {S ∈ P(Nat) | S ⊆ γ(even)}.An under-approximating Galois connection, (P(C), ⊇) α u , γ A op , where A op = (A, A ), is the dual. Here, even ∈ Parity op asserts that all even numbers are included in the program's outputs -a strong assertion. Also, we may reuse γ : A → P(C) as the upper adjoint from A op to P(C) op iff γ preserves joins in (A, A ) -another strong demand.Fortunately, there is an alternative view of under-approximation: a ∈ A op asserts an existential property -there exists an output with property a. For example, even ∈ Parity op asserts "∃even" -there is an even number in the program's outputs, which is a set from {S ∈ P(Nat) | S ∩ γ(even) = ∅}. Now, we can generalize both over-and under-approximation to multiple properties, e.g., ∀{even, odd } ≡ ∀(even ∨ odd ) -all outputs are even-or odd-valued; and ∃{even, odd } ≡ ∃even ∧ ∃odd -the output set includes an even value and an odd value. These examples "lift" A and A op into the powerset lattices, P L (A) and P U (A), respectively, and set the stage for the problem studied in this paper.schmidt@cis.ksu.edu.

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Section: Validation and Refutation Logicsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Closed and Logical Relations for Over- and Under-Approximation of Powersets

Schmidt

2004

Static Analysis

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“…Given a description function ρ : S → S α , the functions α = post(ρ) and γ = pre(ρ) form a Galois connection from 2 S to 2 S α (Proposition 6 of [19]); post and pre are the corresponding post-and preimage relations.…”

Section: Timer Abstraction and Fairnessmentioning

confidence: 99%

“…2L + µ (i.e. formulas of the µ-calculus without negation and containing only the 2 operator) or LTL [19,11].…”

Section: Timer Abstraction and Fairnessmentioning

confidence: 99%

“…Working within the Abstract Interpretation framework guarantees the preservation (in the direction from the abstract to the concrete model) of the truth of formulas of temporal logics without existential quantification over paths, e.g. 2L + µ (i.e., all formulas of the µ-calculus without negation and containing only the 2 operator) or next-free LTL [19,11]. Counterexamples can be spurious.…”

Section: Introductionmentioning

confidence: 99%

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Using Fairness to Make Abstractions Work

Bošnački

Ioustinova

Sidorova

2004

Model Checking Software

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Dragan Bo˘na˘ki C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Software ENgineeringUsing Fairness To Make Abstractions Work Dragan Bosnacki, Natalia Ioustinova, Natalia Sidorova Using Fairness To Make Abstractions Work ABSTRACT Abstractions often introduce infinite traces which have no corresponding traces at the concrete level and can lead to the failure of the verification. Refinement does not always help to eliminate those traces. In this paper, we consider a timer abstraction that introduces a cyclic behaviour on abstract timers and we show how one can exclude cycles by imposing a strong fairness constraint on the abstract model. By employing the fact that the loop on the abstract timer is a self-loop, we render the strong fairness constraint into a weak fairness constraint and embed it into the verification algorithm. We implemented the algorithm in the DTSpin model checker and showed its efficiency on case studies. The same approach can be used for other data abstractions that introduce self-loops. Abstract. Abstractions often introduce infinite traces which have no corresponding traces at the concrete level and can lead to the failure of the verification. Refinement does not always help to eliminate those traces. In this paper, we consider a timer abstraction that introduces a cyclic behaviour on abstract timers and we show how one can exclude cycles by imposing a strong fairness constraint on the abstract model. By employing the fact that the loop on the abstract timer is a self-loop, we render the strong fairness constraint into a weak fairness constraint and embed it into the verification algorithm. We implemented the algorithm in the DT Spin model checker and showed its efficiency on case studies. The same approach can be used for other data abstractions that introduce self-loops. REPORT SEN-E0313 DECEMBER 16, 2003 SEN

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Model Checking

Peled

Spoletini

2009

Wiley Encyclopedia of Computer Science and Engineering

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Model checking is an automatic technique for verifying models of software or hardware systems against their specification. This analysis is based on an exploration of the checked system's state space, hence, it is in general affected by the state explosion problem. In this article, we present the classic model checking approaches and different techniques to deal with the complexity problem. We also describe some popular model checking systems.

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Property preserving abstractions for the verification of concurrent systems

Cited by 281 publications

References 25 publications

Closed and Logical Relations for Over- and Under-Approximation of Powersets

Closed and Logical Relations for Over- and Under-Approximation of Powersets

Using Fairness to Make Abstractions Work

Model Checking

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