Nested interpolants

Heizmann, Matthias; Hoenicke, Jochen; Podelski, Andreas

doi:10.1145/1706299.1706353

Cited by 63 publications

(81 citation statements)

References 20 publications

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“…Heizmann et al [16] propose a procedure that views a program as a nested word automaton. Interpolants or predicate abstraction [12] are used to generalize infeasible paths to error and remove them from the program's automaton until no errors are reachable.…”

Section: Related Workmentioning

confidence: 99%

“…They construct program invariants by generalizing from finite paths through the control flow graph of the program. The most prominent of these are interpolationbased algorithms [27,26,16], introduced by McMillan in [27] and inspired by the success of Craig interpolants [9] for image-approximation in symbolic model checking [25]. In general, interpolation-based software model checking techniques extract interpolants from refutation proofs of infeasible program paths.…”

Section: Introductionmentioning

confidence: 99%

“…Yet, so far, interpolation-based techniques have been limited to intra-procedural analysis [27], restricted to non-recursive programs with bounded loops [26], or not modular in terms of generated proofs [16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Whale: An Interpolation-Based Algorithm for Inter-procedural Verification

Albarghouthi

Gurfinkel

Chećhik

2012

Lecture Notes in Computer Science

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Abstract. In software verification, Craig interpolation has proven to be a powerful technique for computing and refining abstractions. In this paper, we propose an interpolation-based software verification algorithm for checking safety properties of (possibly recursive) sequential programs. Our algorithm, called Whale, produces inter-procedural proofs of safety by exploiting interpolation for guessing function summaries by generalizing under-approximations (i.e., finite traces) of functions. We implemented our algorithm in LLVM and applied it to verifying properties of low-level code written for the pacemaker challenge. We show that our prototype implementation outperforms existing state-of-the-art tools.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Whale: An Interpolation-Based Algorithm for Inter-procedural Verification

Albarghouthi

Gurfinkel

Chećhik

2012

Lecture Notes in Computer Science

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“…In interpolation-based verification approaches, a Craig interpolant [3] is a logical formula justifying why a program trace is spurious and therefore can be used, for example, to refine the set of predicates for predicate abstraction [10], invariant generation [13], and correctness proofs of programs [8]. As refining a path in the control flow graph of a program requires iterative computations of interpolants for each path location, Craig interpolants have been generalized to sequence interpolants for their use in bounded model checking non-procedural programs [10].…”

Section: Introductionmentioning

confidence: 99%

“…Using sequence interpolants to reason about programs with recursive procedures is however a non-trivial task. The work of [12] introduces the notion of tree interpolants, which can be used for the verification of concurrent [5] and recursive programs [8]. In this context, dependencies between program paths are encoded using a tree data structure, where a tree node represents a formula valid at an intermediate program location.…”

Section: Introductionmentioning

confidence: 99%

Tree Interpolation in Vampire

Blanc

Gupta

Kovács

et al. 2013

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. We describe new extensions of the Vampire theorem prover for computing tree interpolants. These extensions generalize Craig interpolation in Vampire, and can also be used to derive sequence interpolants. We evaluated our implementation on a large number of examples over the theory of linear integer arithmetic and integer-indexed arrays, with and without quantifiers. When compared to other methods, our experiments show that some examples could only be solved by our implementation.

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What’s Decidable About Program Verification Modulo Axioms?

Mathur

Madhusudan

Viswanathan

2020

Tools and Algorithms for the Construction and Analysis of Systems

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We consider the decidability of the verification problem of programs modulo axioms -automatically verifying whether programs satisfy their assertions, when the function and relation symbols are interpreted as arbitrary functions and relations that satisfy a set of first-order axioms. Though verification of uninterpreted programs (with no axioms) is already undecidable, a recent work introduced a subclass of coherent uninterpreted programs, and showed that they admit decidable verification [26]. We undertake a systematic study of various natural axioms for relations and functions, and study the decidability of the coherent verification problem. Axioms include relations being reflexive, symmetric, transitive, or total order relations, functions restricted to being associative, idempotent or commutative, and combinations of such axioms as well. Our comprehensive results unearth a rich landscape that shows that though several axiom classes admit decidability for coherent programs, coherence is not a panacea as several others continue to be undecidable. 1 We adapt the definition in a way that preserves the spirit of the definition of coherence. Moreover, if we do not adapt the definition, essentially all axioms classes we study in this paper would be undecidable.

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Nested interpolants

Cited by 63 publications

References 20 publications

Whale: An Interpolation-Based Algorithm for Inter-procedural Verification

Whale: An Interpolation-Based Algorithm for Inter-procedural Verification

Tree Interpolation in Vampire

What’s Decidable About Program Verification Modulo Axioms?

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