Combining theories with shared set operations

  • Authors:

  • Thomas Wies;Ruzica Piskac;Viktor Kuncak

  • Affiliations:

  • EPFL, School of Computer and Communication Sciences, Switzerland;EPFL, School of Computer and Communication Sciences, Switzerland;EPFL, School of Computer and Communication Sciences, Switzerland

  • Venue:
  • FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
  • Year:
  • 2009

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Abstract

Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theorem and apply it to show the decidability of the satisfiability problem for a class of formulas obtained by applying propositional connectives to formulas belonging to: 1) Boolean Algebra with Presburger Arithmetic (with quantifiers over sets and integers), 2) weak monadic second-order logic over trees (with monadic second-order quantifiers), 3) two-variable logic with counting quantifiers (ranging over elements), 4) the Bernays-Schönfinkel-Ramsey class of first-order logic with equality (with ∃*¬* quantifier prefix), and 5) the quantifier-free logic of multisets with cardinality constraints.