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International Conference on Concurrency Theory

CONCUR 2010: CONCUR 2010 - Concurrency Theory pp 373–387Cite as

On the Use of Non-deterministic Automata for Presburger Arithmetic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6269))

Abstract

A well-known decision procedure for Presburger arithmetic uses deterministic finite-state automata. While the complexity of the decision procedure for Presburger arithmetic based on quantifier elimination is known (roughly, there is a double-exponential non-deterministic time lower bound and a triple exponential deterministic time upper bound), the exact complexity of the automata-based procedure was unknown. We show in this paper that it is triple-exponential as well by analysing the structure of the non-deterministic automata obtained during the construction. Furthermore, we analyse the sizes of deterministic and non-deterministic automata built for several subclasses of Presburger arithmetic such as disjunctions and conjunctions of atomic formulas. To retain a canonical representation which is one of the strengths of the use of automata we use residual finite-state automata, a subclass of non-deterministic automata.

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Author information

Authors and Affiliations

  1. LIAFA, CNRS & University Paris Diderot (Paris 7), Case 7014, 75205, Paris 13, France

    Antoine Durand-Gasselin & Peter Habermehl

Authors
  1. Antoine Durand-Gasselin
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  2. Peter Habermehl
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Editor information

Editors and Affiliations

  1. Laboratoire Spécification et Vérification (LSV), ENS de Cachan & CNRS, 94235, Cachan cedex, France

    Paul Gastin

  2. LIAFA, Université Paris Diderot, 75205, Paris cedex, France

    François Laroussinie

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Durand-Gasselin, A., Habermehl, P. (2010). On the Use of Non-deterministic Automata for Presburger Arithmetic. In: Gastin, P., Laroussinie, F. (eds) CONCUR 2010 - Concurrency Theory. CONCUR 2010. Lecture Notes in Computer Science, vol 6269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15375-4_26

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  • DOI: https://doi.org/10.1007/978-3-642-15375-4_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15374-7

  • Online ISBN: 978-3-642-15375-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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