Effective Quantifier Elimination for Presburger Arithmetic with Infinity

Authors:
Aless Lasaruk;Thomas Sturm
Affiliations:
FORWISS, Universität Passau, Passau, Germany 94030;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Santander, Spain 39071
Venue:
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Year:
2009

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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.