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Resolution proof transformation for compression and interpolation

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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.

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Notes

  1. Full experimental data, as well as executables used in tests are available at http://verify.inf.usi.ch/sites/default/files/FMSD2014.tar.gz

    Table 1 Results for SMT benchmarks
    Full size table

  2. Full experimental data, as well as executables used in tests are available at http://verify.inf.usi.ch/sites/default/files/FMSD2014.tar.gz

  3. Note that in practice flattening can be avoided. For instance in Example 5 we do not perform any flattening.

  4. The benchmarks and the detailed results are available at http://verify.inf.usi.ch/sites/default/files/FMSD2014.tar.gz

  5. Notice that in some cases \(AB\)-mixed predicates were produced during the search, but they did not appear in the proof.

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Authors and Affiliations

  1. University of Lugano, Lugano, Switzerland

    Simone Fulvio Rollini & Natasha Sharygina

  2. Atrenta Advanced R&D of Grenoble, Grenoble, France

    Roberto Bruttomesso

  3. Phonak, Stäfa, Switzerland

    Aliaksei Tsitovich

Authors
  1. Simone Fulvio Rollini
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  2. Roberto Bruttomesso
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  3. Natasha Sharygina
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  4. Aliaksei Tsitovich
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Correspondence to Simone Fulvio Rollini.

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Rollini, S.F., Bruttomesso, R., Sharygina, N. et al. Resolution proof transformation for compression and interpolation. Form Methods Syst Des 45, 1–41 (2014). https://doi.org/10.1007/s10703-014-0208-x

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