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On Superposition-Based Satisfiability Procedures and Their Combination

  • Hélène Kirchner
  • Silvio Ranise
  • Christophe Ringeissen
  • Duc Khanh Tran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3722)

Abstract

We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.

Keywords

Combination Method Elementary Equality Proof Obligation Unit Clause Empty Clause 
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-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hélène Kirchner
    • 1
  • Silvio Ranise
    • 1
  • Christophe Ringeissen
    • 1
  • Duc Khanh Tran
    • 1
  1. 1.LORIA & INRIA-Lorraine 

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