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Decidability and Undecidability Results for Nelson-Oppen and Rewrite-Based Decision Procedures

  • Maria Paola Bonacina
  • Silvio Ghilardi
  • Enrica Nicolini
  • Silvio Ranise
  • Daniele Zucchelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)

Abstract

In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite models, respectively. We exhibit a theory T 1 such that satisfiability is decidable, but satisfiability in infinite models is undecidable. It follows that satisfiability in T 1T 2 is undecidable, whenever T 2 has only infinite models, even if signatures are disjoint and satisfiability in T 2 is decidable.

In the second part of the paper we strengthen the Nelson-Oppen decidability transfer result, by showing that it applies to theories over disjoint signatures, whose satisfiability problem, in either arbitrary or infinite models, is decidable. We show that this result covers decision procedures based on rewriting, complementing recent work on combination of theories in the rewrite-based approach to satisfiability.

Keywords

Turing Machine Decision Procedure Automate Reasoning Predicate Symbol Cardinality Constraint 
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 2006

Authors and Affiliations

  • Maria Paola Bonacina
    • 1
  • Silvio Ghilardi
    • 2
  • Enrica Nicolini
    • 3
  • Silvio Ranise
    • 2
    • 4
  • Daniele Zucchelli
    • 2
    • 4
  1. 1.Dipartimento di InformaticaUniversitá degli Studi di VeronaItalia
  2. 2.Dipartimento di InformaticaUniversitá degli Studi di MilanoItalia
  3. 3.Dipartimento di MatematicaUniversitá degli Studi di MilanoItalia
  4. 4.LORIA & INRIA-LorraineNancyFrance

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