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International Workshop on Computer Algebra in Scientific Computing

CASC 2009: Computer Algebra in Scientific Computing pp 195–212Cite as

Effective Quantifier Elimination for Presburger Arithmetic with Infinity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

Abstract

We consider Presburger arithmetic extended by infinity. For this we give an effective quantifier elimination and decision procedure which implies also the completeness of our extension. The asymptotic worst-case complexity of our procedure is bounded by a function that is triply exponential in the input word length, which is known to be a tight bound for regular Presburger arithmetic. Possible application areas include quantifier elimination and decision procedures for Boolean algebras with cardinality constraints, which have recently moved into the focus of computer science research for software verification, and deductive database queries.

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Author information

Authors and Affiliations

  1. FORWISS, Universität Passau, 94030, Passau, Germany

    Aless Lasaruk

  2. Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071, Santander, Spain

    Thomas Sturm

Authors
  1. Aless Lasaruk
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  2. Thomas Sturm
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

    Vladimir P. Gerdt

  2. Technische Universität München‘, Institut für Informatik, Garching, Germany

    Ernst W. Mayr

  3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Lasaruk, A., Sturm, T. (2009). Effective Quantifier Elimination for Presburger Arithmetic with Infinity. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_18

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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