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Formal Methods in System Design

, Volume 45, Issue 1, pp 1–41 | Cite as

Resolution proof transformation for compression and interpolation

  • Simone Fulvio Rollini
  • Roberto Bruttomesso
  • Natasha Sharygina
  • Aliaksei Tsitovich
Article

Abstract

Verification methods based on SAT, SMT, and theorem proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal reason that led to unsatisfiability, for computing abstractions, or for deriving Craig interpolants. In this paper we focus on two important aspects that concern efficient handling of proofs of unsatisfiability: compression and manipulation. First of all, since the proof size can be very large in general (exponential in the size of the input problem), it is indeed beneficial to adopt techniques to compress it for further processing. Secondly, proofs can be manipulated as a flexible preprocessing step in preparation for interpolant computation. Both these techniques are implemented in a framework that makes use of local rewriting rules to transform the proofs. We show that a careful use of the rules, combined with existing algorithms, can result in an effective simplification of the original proofs. We have evaluated several heuristics on a wide range of unsatisfiable problems deriving from SAT and SMT test cases.

Keywords

Resolution system Craig interpolation Proof compression  Formal verification 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Simone Fulvio Rollini
    • 1
  • Roberto Bruttomesso
    • 2
  • Natasha Sharygina
    • 1
  • Aliaksei Tsitovich
    • 3
  1. 1.University of LuganoLuganoSwitzerland
  2. 2.Atrenta Advanced R&D of GrenobleGrenobleFrance
  3. 3.PhonakStäfaSwitzerland

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