A Complete Abstract Interpretation Framework for Coverability Properties of WSTS

Ganty, Pierre; Raskin, Jean-François; Begin, Laurent Van

doi:10.1007/11609773_4

Cited by 29 publications

(35 citation statements)

References 22 publications

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“…This means that, in theory, the complexity of this problem is high, but in practice, there are quite efficient techniques (based on iterative computation of under/upper approximations) developed recently for solving this problem which have been implemented and used successfully in [GRB06b,GRB06a]. Moreover, we have proposed a notion of stratified context-bounding for which the verification is in NP, i.e., as hard as in the case without dynamic thread creation.…”

Section: Resultsmentioning

confidence: 99%

Context-Bounded Analysis for Concurrent Programs with Dynamic Creation of Threads

Atig

Bouajjani

Qadeer

2009

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Context-bounded analysis has been shown to be both efficient and effective at finding bugs in concurrent programs. According to its original definition, contextbounded analysis explores all behaviors of a concurrent program up to some fixed number of context switches between threads. This definition is inadequate for programs that create threads dynamically because bounding the number of context switches in a computation also bounds the number of threads involved in the computation. In this paper, we propose a more general definition of context-bounded analysis useful for programs with dynamic thread creation. The idea is to bound the number of context switches for each thread instead of bounding the number of switches of all threads. We consider several variants based on this new definition, and we establish decidability and complexity results for the analysis induced by them.

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Section: Resultsmentioning

confidence: 99%

Context-Bounded Analysis for Concurrent Programs with Dynamic Creation of Threads

Atig

Bouajjani

Qadeer

2009

Tools and Algorithms for the Construction and Analysis of Systems

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“…We give a positive answer for the case of so-called well-structured systems. This class, which contains broadcast protocols and other interesting infinite-state models, is wellinvestigated [5][6][7][8][9]. The corresponding verification problem (called coverability) is known to be decidable [10].…”

Section: Introductionmentioning

confidence: 99%

Is Lazy Abstraction a Decision Procedure for Broadcast Protocols?

Dimitrova

Podelski

Lecture Notes in Computer Science

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Abstract. Lazy abstraction builds up an abstract reachability tree by locally refining abstractions in order to eliminate spurious counterexamples in smaller and smaller subtrees. The method has proven useful to verify systems code. It is still open how good the method is as a decision procedure, i.e., whether the method terminates for already known decidable verification problems. In this paper, we answer the question positively for broadcast protocols and other infinite-state models in the class of so-called well-structured systems. This extends an existing result on systems with a finite bisimulation quotient.

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“…Therefore, many attempts have been made at deriving complete forward algorithms for this problem. The most general solutions are described in [16] and [15]. The expand, enlarge, and check algorithm [16] decides the covering problem using a combination of an underapproximating and an over-approximating forward analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The over-approximating analysis relies on a so-called adequate domain of limits for the representation of downward-closed sets, which is actually the ideal completion of the underlying well-quasi ordering [12]. Ganty et al propose an alternative algorithm [15] based on abstract interpretation. Unlike our approach, this algorithm uses a finite abstract domain that represents downward-closed sets by complements of upward-closed sets.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm then relies on a complete refinement scheme to refine the abstraction for a specific coverability goal. Both algorithms [12,15] compute an over-approximation of the covering set as a byproduct of the analysis, namely an invariant whose complement contains the coverability goal. To ensure completeness, the precision of this computed invariant is geared towards proving the specific instance of the coverability problem.…”

Section: Introductionmentioning

confidence: 99%

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Ideal Abstractions for Well-Structured Transition Systems

Zufferey

Wies

Henzinger

2012

Lecture Notes in Computer Science

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Abstract. Many infinite state systems can be seen as well-structured transition systems (WSTS), i.e., systems equipped with a well-quasi-ordering on states that is also a simulation relation. WSTS are an attractive target for formal analysis because there exist generic algorithms that decide interesting verification problems for this class. Among the most popular algorithms are acceleration-based forward analyses for computing the covering set. Termination of these algorithms can only be guaranteed for flattable WSTS. Yet, many WSTS of practical interest are not flattable and the question whether any given WSTS is flattable is itself undecidable. We therefore propose an analysis that computes the covering set and captures the essence of acceleration-based algorithms, but sacrifices precision for guaranteed termination. Our analysis is an abstract interpretation whose abstract domain builds on the ideal completion of the well-quasi-ordered state space, and a widening operator that mimics acceleration and controls the loss of precision of the analysis. We present instances of our framework for various classes of WSTS. Our experience with a prototype implementation indicates that, despite the inherent precision loss, our analysis often computes the precise covering set of the analyzed system.

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A Complete Abstract Interpretation Framework for Coverability Properties of WSTS

Cited by 29 publications

References 22 publications

Context-Bounded Analysis for Concurrent Programs with Dynamic Creation of Threads

Context-Bounded Analysis for Concurrent Programs with Dynamic Creation of Threads

Is Lazy Abstraction a Decision Procedure for Broadcast Protocols?

Ideal Abstractions for Well-Structured Transition Systems

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