Industrial-strength certified SAT solving through verified SAT proof checking

  • Authors:

  • Ashish Darbari;Bernd Fischer;João Marques-Silva

  • Affiliations:

  • ARM, Cambridge, England;School of Electronics and Computer Science, University of Southampton, Southampton, UK;School of Computer Science and Informatics, University College Dublin, Dublin 4, Ireland

  • Venue:
  • ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
  • Year:
  • 2010

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Abstract

Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form of assurance for the results, as the solvers can (and sometimes do) have bugs. Unfortunately, the complexity of modern and highly optimized SAT solvers renders impractical the development of direct formal proofs of their correctness. This paper presents an alternative approach where an untrusted, industrial-strength, SAT solver is plugged into a trusted, formally verified, SAT proof checker to provide industrial-strength certified SAT solving. The key characteristics of our approach are (i) that the checker is not tied to a specific SAT solver but certifies any solver respecting the agreed format for satisfiability and unsatisfiability claims, (ii) that the checker is automatically extracted from the formal development, and (iii) that the combined system can be used as a standalone executable program independent of any supporting theorem prover. The core of the system is a checker for unsatisfiability claims that is formally designed and verified in Coq. We present its formal design and outline the correctness criteria. The actual standalone checker is automatically extracted from the the Coq development. An evaluation of the checker on a representative set of industrial benchmarks from the SAT Race Competition shows that, albeit it is slower than uncertified SAT checkers, it is significantly faster than certified checkers implemented on top of an interactive theorem prover.