Combining Theories with Shared Set Operations

  • Thomas Wies
  • Ruzica Piskac
  • Viktor Kuncak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5749)


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.


Decision Procedure Cardinality Constraint Tree Automaton Star Type Linear Arithmetic 
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 2009

Authors and Affiliations

  • Thomas Wies
    • 1
  • Ruzica Piskac
    • 1
  • Viktor Kuncak
    • 1
  1. 1.EPFL School of Computer and Communication SciencesSwitzerland

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