Resolution proof transformation for compression and interpolation

• Published in: Formal methods in system design Vol. 45; no. 1; pp. 1 - 41
• Main Authors: Rollini, Simone Fulvio, Bruttomesso, Roberto, Sharygina, Natasha, Tsitovich, Aliaksei
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.08.2014
• Subjects: CAE) and Design; Circuits and Systems; Computer-Aided Engineering (CAD; Electrical Engineering; Engineering; Software Engineering/Programming and Operating Systems; Proof compression; Resolution system; Craig interpolation; Formal verification
• ISSN: 0925-9856; 1572-8102
• DOI: 10.1007/s10703-014-0208-x

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.