Beautiful Interpolants

Albarghouthi, Aws; McMillan, Kenneth L.

doi:10.1007/978-3-642-39799-8_22

Cited by 59 publications

(81 citation statements)

References 29 publications

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“…For linear real arithmetic, this can be performed by constructing a system of constraints whose solution is a proof of unsatisfiability (and an interpolant) [53]. As recently shown [2], the simplicity of the proof can be crucial to discovering the predicates required for a safe inductive invariant. Finding simple proofs boils down to finding an optimal solution of the system of constraints.…”

Section: Applications Of Optimizationmentioning

confidence: 99%

“…Finding simple proofs boils down to finding an optimal solution of the system of constraints. Using SYMBA, this can be automated, without the need for the heuristics employed in [2].…”

Section: Applications Of Optimizationmentioning

confidence: 99%

“…the satisfying assignments of ϕ. 2 Note that we are optimizing a set of objective functions, as opposed to a single function as in traditional optimization problems. This allows SYMBA to reuse information computed for one objective in order to speed up the optimization of other objectives.…”

Section: Applications Of Optimizationmentioning

confidence: 99%

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Symbolic optimization with SMT solvers

Albarghouthi

Kincaid

et al. 2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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101

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The rise in efficiency of Satisfiability Modulo Theories (SMT) solvers has created numerous uses for them in software verification, program synthesis, functional programming, refinement types, etc. In all of these applications, SMT solvers are used for generating satisfying assignments (e.g., a witness for a bug) or proving unsatisfiability/validity (e.g., proving that a subtyping relation holds). We are often interested in finding not just an arbitrary satisfying assignment, but one that optimizes (minimizes/maximizes) certain criteria. For example, we might be interested in detecting program executions that maximize energy usage (performance bugs), or synthesizing short programs that do not make expensive API calls. Unfortunately, none of the available SMT solvers offer such optimization capabilities.In this paper, we present SYMBA, an efficient SMT-based optimization algorithm for objective functions in the theory of linear real arithmetic (LRA). Given a formula ϕ and an objective function t, SYMBA finds a satisfying assignment of ϕ that maximizes the value of t. SYMBA utilizes efficient SMT solvers as black boxes. As a result, it is easy to implement and it directly benefits from future advances in SMT solvers. Moreover, SYMBA can optimize a set of objective functions, reusing information between them to speed up the analysis. We have implemented SYMBA and evaluated it on a large number of optimization benchmarks drawn from program analysis tasks. Our results indicate the power and efficiency of SYMBA in comparison with competing approaches, and highlight the importance of its multi-objective-function feature.

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Section: Applications Of Optimizationmentioning

confidence: 99%

“…Finding simple proofs boils down to finding an optimal solution of the system of constraints. Using SYMBA, this can be automated, without the need for the heuristics employed in [2].…”

Section: Applications Of Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Symbolic optimization with SMT solvers

Albarghouthi

Kincaid

et al. 2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Self Cite

101

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“…A recent paper proposes the generation of beautiful interpolants [1], which are interpolants with particularly simple shape and Boolean structure; empirically, interpolants of this kind were found to be beneficial for the convergence of model checkers. Domainspecific knowledge is not explicitly used when computing beautiful interpolants, but it is possible to use the procedure in [1] in combination with our abstraction framework.…”

Section: Related Workmentioning

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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“…It is a variant of [4], and is a special case of interpolants generated as a side-effect of IC3 [3,2,14]. Variants and extensions have been examined for richer theories, such as arithmetic [1,7]. Let A and B be two propositional formulas, whose conjunction is unsatisfiable.…”

Section: Propositional Zipper Interpolationmentioning

confidence: 99%

Instantiations, Zippers and EPR Interpolation

Bjørner

Gurfinkel

Korovin

et al.

EPiC Series in Computing

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This paper describes interpolation procedures for EPR. In principle, interpolation for EPR is simple: It is a special case of first-order interpolation. In practice, we would like procedures that take advantage of properties of EPR: EPR admits finite models and those models are sometimes possible to describe very compactly. Inspired by procedures for propositional logic that use models and cores, but not proofs, we develop a procedure for EPR that uses just models and cores.

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Beautiful Interpolants

Cited by 59 publications

References 29 publications

Symbolic optimization with SMT solvers

Symbolic optimization with SMT solvers

Guiding Craig interpolation with domain-specific abstractions

Instantiations, Zippers and EPR Interpolation

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