Complexity of pattern-based verification for multithreaded programs

Esparza, Javier; Ganty, Pierre

doi:10.1145/1925844.1926443

Cited by 22 publications

(30 citation statements)

References 31 publications

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“…This approach has been used successfully in verification [19], [21], [26], [28], [31], and it seems natural to extend it to querying paths in graph databases.…”

Section: Introductionmentioning

confidence: 99%

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Figueira

Libkin

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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We study logics expressing properties of paths in graphs that are tailored to querying graph databases: a data model for new applications such as social networks, the Semantic Web, biological data, crime detection, and others. The basic construct of such logics, a regular path query, checks for paths whose labels belong to a regular language. These logics fail to capture two commonly needed features: counting properties, and the ability to compare paths. It is known that regular path-comparison relations (e.g., prefix or equality) can be added without significant complexity overhead; however, adding common relations often demanded by applications (e.g., subword, subsequence, suffix) results in either undecidability or astronomical complexity.We propose, as a way around this problem, to use automata with counting functionalities, namely Parikh automata. They express many counting properties directly, and they approximate many relations of interest. We prove that with Parikh automata defining both languages and relations used in queries, we retain the low complexity of the standard path logics for graphs. In particular, this gives us efficient approximations to queries with prohibitively high complexity. We extend the best known decidability results by showing that even more expressive classes of relations are possible in query languages (sometimes with restriction on the shape of formulae). We also show that Parikh automata admit two convenient representations by analogs of regular expressions, making them usable in real-life querying.

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“…This approach has been used successfully in verification [19], [21], [26], [28], [31], and it seems natural to extend it to querying paths in graph databases.…”

Section: Introductionmentioning

confidence: 99%

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Figueira

Libkin

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…In contrast, our results are applicable even if the boundedness property does not hold. Recently, Esparza and Ganty [6] introduced a technique for verification of multithreaded programs based on patterns which are expressions of the form w * 1 · · · w * m . For multithreaded reachability, context-bounded reachability [20,22] is a popular underapproximation technique which tackles the undecidability by limiting the search to those runs where the active thread changes at most k times.…”

Section: Reachability Analysis Of Programs With Counters and Proceduresmentioning

confidence: 99%

“…With respect to the complexity, it is shown in [6] that given an effective representation of B and L 1 , . .…”

Section: Lemma 15 Given a Bounded Expressionmentioning

confidence: 99%

“…A more detailed analysis shows that, unless NP = P, k-context reachability is exponential in k but polynomial in the program size. In [6], it is shown that pattern based reachability (i.e., where the bounded expression B is fixed a priori, and which reduces to the problem of Lemma 15 in polynomial time) is also NP-complete. Moreover, the authors show that, unless NP = P, pattern-based reachability is exponential in the number of threads, the size of the bounded expression, and the maximum number of procedures per thread, but is polynomial in the maximum size of a procedure.…”

Section: Propositionmentioning

confidence: 99%

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Bounded underapproximations

Ganty

Majumdar

Monmege

2012

Form Methods Syst Des

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International audienceWe show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L'⊆L which has the same Parikh (commutative) image as L. Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form w1*w2*... wm* for some w1,...,wm∈ Σ*. In particular bounded context-free languages have nice structural and decidability properties. Our proof proceeds in two parts. First, we give a new construction that shows that each context free language L has a subset LN that has the same Parikh image as L and that can be represented as a sequence of substitutions on a linear language. Second, we inductively construct a Parikh-equivalent bounded context-free subset of LN. We show two applications of this result in model checking: to underapproximate the reachable state space of multithreaded procedural programs and to underapproximate the reachable state space of recursive counter programs. The bounded language constructed above provides a decidable underapproximation for the original problems. By iterating the construction, we get a semi-algorithm for the original problems that constructs a sequence of underapproximations such that no two underapproximations of the sequence can be compared. This provides a progress guarantee: every word w∈L is in some underapproximation of the sequence, and hence, a program bug is guaranteed to be found. In particular, we show that verification with bounded languages generalizes context-bounded reachability for multithreaded programs

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“…The state-reachability problem for multi-threaded programs is PSPACE-complete [21] with a finite number of finite-state threads, and undecidable [29] with recursive threads. Current analysis approaches either explore an underapproximate concurrent semantics by considering relatively few interleavings [9,22] or explore a coarse overapproximate semantics via abstraction [13,18].…”

Section: Introductionmentioning

confidence: 99%

Analysis of recursively parallel programs

Bouajjani

Emmi

2012

Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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We propose a general formal model of isolated hierarchical parallel computations, and identify several fragments to match the concurrency constructs present in real-world programming languages such as Cilk and X10. By associating fundamental formal models (vector addition systems with recursive transitions) to each fragment, we provide a common platform for exposing the relative difficulties of algorithmic reasoning. For each case we measure the complexity of deciding state-reachability for finite-data recursive programs, and propose algorithms for the decidable cases. The complexities which include PTIME, NP, EXPSPACE, and 2EXPTIME contrast with undecidable state-reachability for recursive multi-threaded programs.

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Complexity of pattern-based verification for multithreaded programs

Cited by 22 publications

References 31 publications

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Bounded underapproximations

Analysis of recursively parallel programs

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