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A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories

  • Alessandro Cimatti
  • Alberto Griggio
  • Roberto Sebastiani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4501)

Abstract

Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. Surprisingly, the same problem in the context of SAT Modulo Theories (SMT) has instead received very little attention in the literature; in particular, we are not aware of any work aiming at producing small unsatisfiable cores in SMT.

The purpose of this paper is to start filling the gap in this area, by proposing a novel approach for computing small unsat cores in SMT. The main idea is to combine an SMT solver with an external propositional core extractor: the SMT solver produces the theory lemmas found during the search; the core extractor is then called on the boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas have been removed.

The approach has several advantages: it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play way, so that to benefit for free of all unsat-core reduction techniques which have been or will be made available.

Keywords

Truth Assignment Propositional Formula Input Formula Core Extractor Unsatisfiable Core 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alessandro Cimatti
    • 1
  • Alberto Griggio
    • 2
  • Roberto Sebastiani
    • 2
  1. 1.ITC-IRST, Povo, TrentoItaly
  2. 2.DIT, Università di TrentoItaly

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