Refinement of Trace Abstraction

Heizmann, Matthias; Hoenicke, Jochen; Podelski, Andreas

doi:10.1007/978-3-642-03237-0_7

Cited by 91 publications

(81 citation statements)

References 17 publications

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“…Language-theoretic program verification The method presented in this paper is inspired by the language-theoretic approach to program correctness proposed in [21]. Notably, this approach has also been used in the context of concurrent programs with a fixed number of threads [14] and concurrent programs with unboundedly many threads [15].…”

Section: Related Workmentioning

confidence: 99%

“…Notably, this approach has also been used in the context of concurrent programs with a fixed number of threads [14] and concurrent programs with unboundedly many threads [15]. One fundamental difference between our approach and previous language-theoretic techniques is that in [14,15,21], a finite set of program statements and therefore a finite alphabet was used. In [15], counting proofs were presented as a method for automatically synthesizing auxiliary variables in complex counting arguments for parameterized protocols.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Proof Spaces for Unbounded Parallelism

Farzan

Kincaid

Podelski

2015

Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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In this paper, we present a new approach to automatically verify multi-threaded programs which are executed by an unbounded number of threads running in parallel.The starting point for our work is the problem of how we can leverage existing automated verification technology for sequential programs (abstract interpretation, Craig interpolation, constraint solving, etc.) for multi-threaded programs. Suppose that we are given a correctness proof for a trace of a program (or for some other program fragment). We observe that the proof can always be decomposed into a finite set of Hoare triples, and we ask what can be proved from the finite set of Hoare triples using only simple combinatorial inference rules (without access to a theorem prover and without the possibility to infer genuinely new Hoare triples)?We introduce a proof system where one proves the correctness of a multi-threaded program by showing that for each trace of the program, there exists a correctness proof in the space of proofs that are derivable from a finite set of axioms using simple combinatorial inference rules. This proof system is complete with respect to the classical proof method of establishing an inductive invariant (which uses thread quantification and control predicates). Moreover, it is possible to algorithmically check whether a given set of axioms is sufficient to prove the correctness of a multi-threaded program, using ideas from well-structured transition systems.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Proof Spaces for Unbounded Parallelism

Farzan

Kincaid

Podelski

2015

Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Self Cite

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show abstract

“…The work in [17,18] presents an automatatheoretic approach to the analysis and verification of sequential and recursive programs. The present paper continues this line of work and extends it to concurrent programs.…”

Section: Related Workmentioning

confidence: 99%

Inductive data flow graphs

Farzan

Kincaid

Podelski

2013

Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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The correctness of a sequential program can be shown by the annotation of its control flow graph with inductive assertions. We propose inductive data flow graphs, data flow graphs with incorporated inductive assertions, as the basis of an approach to verifying concurrent programs. An inductive data flow graph accounts for a set of dependencies between program actions in interleaved thread executions, and therefore stands as a representation for the set of concurrent program traces which give rise to these dependencies. The approach first constructs an inductive data flow graph and then checks whether all program traces are represented. The size of the inductive data flow graph is polynomial in the number of data dependencies (in a sense that can be made formal); it does not grow exponentially in the number of threads unless the data dependencies do. The approach shifts the burden of the exponential explosion towards the check whether all program traces are represented, i.e., to a combinatorial problem (over finite graphs).

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“…The idea of generalizing spurious error traces was introduced also in [18], by extending an infeasible trace, labeled with interpolants, into a finite interpolant automaton. The method of [18] exploits the fact that some interpolants obtained from the infeasibility proof happen to be inductive w.r.t.…”

Section: Related Workmentioning

confidence: 99%

“…The method of [18] exploits the fact that some interpolants obtained from the infeasibility proof happen to be inductive w.r.t. loops in the program.…”

Section: Related Workmentioning

confidence: 99%

Accelerating Interpolants

Hojjat

Iosif

Konecny

et al. 2012

Automated Technology for Verification and Analysis

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Abstract. We present Counterexample-Guided Accelerated Abstraction Refinement (CEGAAR), a new algorithm for verifying infinite-state transition systems. CEGAAR combines interpolation-based predicate discovery in counterexampleguided predicate abstraction with acceleration technique for computing the transitive closure of loops. CEGAAR applies acceleration to dynamically discovered looping patterns in the unfolding of the transition system, and combines overapproximation with underapproximation. It constructs inductive invariants that rule out an infinite family of spurious counterexamples, alleviating the problem of divergence in predicate abstraction without losing its adaptive nature. We present theoretical and experimental justification for the effectiveness of CE-GAAR, showing that inductive interpolants can be computed from classical Craig interpolants and transitive closures of loops. We present an implementation of CEGAAR that verifies integer transition systems. We show that the resulting implementation robustly handles a number of difficult transition systems that cannot be handled using interpolation-based predicate abstraction or acceleration alone.

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Refinement of Trace Abstraction

Cited by 91 publications

References 17 publications

Proof Spaces for Unbounded Parallelism

Proof Spaces for Unbounded Parallelism

Inductive data flow graphs

Accelerating Interpolants

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