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International Symposium on Frontiers of Combining Systems

FroCoS 2009: Frontiers of Combining Systems pp 366–382Cite as

Combining Theories with Shared Set Operations

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 5749)

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.

Keywords

  • 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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Author information

Authors and Affiliations

  1. EPFL School of Computer and Communication Sciences, Switzerland

    Thomas Wies, Ruzica Piskac & Viktor Kuncak

Authors
  1. Thomas Wies
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  2. Ruzica Piskac
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  3. Viktor Kuncak
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Silvio Ghilardi

  2. Dipartemento di Ingegneria e Scienza dell’Informazione, Università di Trento, Facoltà di Scienze, Via Sommarive 14, 38050, Povo, Trento, Italy

    Roberto Sebastiani

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Wies, T., Piskac, R., Kuncak, V. (2009). Combining Theories with Shared Set Operations. In: Ghilardi, S., Sebastiani, R. (eds) Frontiers of Combining Systems. FroCoS 2009. Lecture Notes in Computer Science(), vol 5749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04222-5_23

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  • DOI: https://doi.org/10.1007/978-3-642-04222-5_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04221-8

  • Online ISBN: 978-3-642-04222-5

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