Effective Quantifier Elimination for Presburger Arithmetic with Infinity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5743)


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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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.FORWISSUniversität PassauPassauGermany
  2. 2.Departamento de Matemáticas, Estadística y Computación, Facultad de CienciasUniversidad de CantabriaSantanderSpain

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