Extending a Verified Simplex Algorithm

Thiemann, René

doi:10.29007/5vlq

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…In this paper, we propose to verify, using Isabelle/HOL [30], a purely functional prover based on ordered resolution. Although our primary interest is in metatheory per se, there are of course applications for verified provers [50].…”

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confidence: 99%

A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness. Methodologically, we apply stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for first-order logic. CCS Concepts • Theory of computation → Logic and verification; Automated reasoning;

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confidence: 99%

A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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“…The main difference is that the conflicts generated are not the negation of the trail, but clauses implied by the theory. The theory of linear integer arithmetic (LA) has already been verified in Isabelle/HOL by Thiemann [5,25], so proving correctness of CDCL(LA) does not need a from-scratch new effort.…”

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confidence: 99%

A Verified SAT Solver Framework including Optimization and Partial Valuations

Fleury¹,

Weidenbach²

EPiC Series in Computing

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Based on our formal framework for CDCL (conflict-driven clause learning) using the proof assistant Isabelle/HOL, we verify an extension of CDCL computing cost-minimal models called OCDCL. It is based on branch and bound and computes models of minimal cost with respect to total valuations. The verification starts by developing a framework for CDCL with branch and bound, called CDCLBnB, which is then instantiated to get OCDCL. We then apply our formalization to three different applications. Firstly, through the dual rail encoding, we reduce the search for cost-optimal models with respect to partial valuations to searching for total cost-optimal models, as derived by OCDCL. Secondly, we instantiate OCDCL to solve MAX-SAT, and, thirdly, CDCLBnB to compute a set of covering models. A large part of the original CDCL verification framework was reused without changes to reduce the complexity of the new formalization. To the best of our knowledge, this is the first rigorous formalization of CDCL with branch and bound and its application to an optimizing CDCL calculus, and the first solution that computes cost-optimal models with respect to partial valuations.

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Extending a Verified Simplex Algorithm

Cited by 2 publications

References 8 publications

A verified prover based on ordered resolution

A verified prover based on ordered resolution

A Verified SAT Solver Framework including Optimization and Partial Valuations

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