An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

Brillout, Angelo; Kroening, Daniel; Rümmer, Philipp; Wahl, Thomas

doi:10.1007/978-3-642-14203-1_33

Cited by 47 publications

(89 citation statements)

References 17 publications

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“…We have implemented CEGAAR by building on the predicate abstraction engine Eldarica 8 [20], the FLATA verifier 9 [20] based on acceleration, and the Princess interpolating theorem prover [11,25]. Tables in Figure 6 compares the performance of the Flata, Eldarica, static acceleration and CEGAAR on a number of benchmarks (the platorm used for experiments is Intel ® Core ™ 2 Duo CPU P8700, 2.53GHz with 4GB of RAM).…”

Section: Resultsmentioning

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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Section: Resultsmentioning

confidence: 99%

Accelerating Interpolants

Hojjat

Iosif

Konecny

et al. 2012

Automated Technology for Verification and Analysis

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“…An occurrence of a term is then called positive if the term (or a positive multiple of the term) is on the right-hand side of ≤, and negative if it is on the left-hand side. By checking the individual proof rules in [10], we can observe that the resulting interpolant I[x 1 , . .…”

Section: Definition 5 (Inequality Interpolation Abstraction)mentioning

confidence: 99%

Guiding Craig interpolation with domain-specific abstractions

2015

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PostprintThis is the accepted version of a paper published in Acta Informatica. This paper has been peerreviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Leroux, J., Rümmer, P., Subotic, P. (2016) Guiding Craig interpolation with domain-specific abstractions. Abstract Craig Interpolation is a standard method to construct and refine abstractions in model checking. To obtain abstractions that are suitable for the verification of software programs or hardware designs, model checkers rely on theorem provers to find the right interpolants, or interpolants containing the right predicates, in a generally infinite lattice of interpolants for any given interpolation problem. We present a semantic and solver-independent framework for systematically exploring interpolant lattices, based on the notion of interpolation abstraction. We discuss how interpolation abstractions can be constructed for a variety of logics, and how they can be applied in the context of software model checking.

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“…Eldarica refines abstractions with the help of Craig Interpolants, extracted from infeasibility proofs for spurious counterexamples. The complete interpolation procedure for Presburger arithmetic was proposed in [4], and is implemented as part of Princess.…”

Section: The Ints Infrastructurementioning

confidence: 99%

A Verification Toolkit for Numerical Transition Systems

Hojjat

Konecny

Garnier

et al. 2012

Lecture Notes in Computer Science

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Abstract. This paper presents a publicly available toolkit and a benchmark suite for rigorous verification of Integer Numerical Transition Systems (INTS), which can be viewed as control-flow graphs whose edges are annotated by Presburger arithmetic formulas. We present FLATA and ELDARICA, two verification tools for INTS. The FLATA system is based on precise acceleration of the transition relation, while the ELDARICA system is based on predicate abstraction with interpolation-based counterexample-driven refinement. The ELDARICA verifier uses the PRINCESS theorem prover as a sound and complete interpolating prover for Presburger arithmetic. Both systems can solve several examples for which previous approaches failed, and present a useful baseline for verifying integer programs. The infrastructure is a starting point for rigorous benchmarking, competitions, and standardized communication between tools.

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An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

Cited by 47 publications

References 17 publications

Accelerating Interpolants

Accelerating Interpolants

Guiding Craig interpolation with domain-specific abstractions

A Verification Toolkit for Numerical Transition Systems

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