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On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables

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Automated Reasoning (IJCAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2083))

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Abstract

This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on in finite words, but this involves some difficult and delicate to implement algorithms. The contribution of this paper is to show, using topological arguments, that only a restricted class of automata on in finite words are necessary for handling real and integer linear arithmetic. This allows the use of substantially simpler algorithms and opens the path to the implementation of a usable system for handling this combined theory.

This work was partially funded by a grant of the “Communautéfrançaise de Belgique - Direction de la recherche scientifique - Actions de recherche concertées”

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Author information

Authors and Affiliations

  1. Université de Liège, Institut Montefiore, B28, 4000, Liège, Belgium

    Bernard Boigelot, Sébastien Jodogne & Pierre Wolper

Authors
  1. Bernard Boigelot
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  2. Sébastien Jodogne
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  3. Pierre Wolper
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Editor information

Editors and Affiliations

  1. Automated Reasoning Project and Department of Computer Science, Australian National University, Canberra, ACT, 0200, Australia

    Rajeev Goré

  2. AG Theoretische Informatik und Logik, Institut für Computersprachen, Technische Universität Wien, Favoritenstr. 9, E185-2, 1040, Wien, Austria

    Alexander Leitsch

  3. Institut für Informatik, Technische Universität München, 80290, München, Germany

    Tobias Nipkow

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© 2001 Springer-Verlag Berlin Heidelberg

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Boigelot, B., Jodogne, S., Wolper, P. (2001). On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables. In: Goré, R., Leitsch, A., Nipkow, T. (eds) Automated Reasoning. IJCAR 2001. Lecture Notes in Computer Science, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45744-5_50

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  • DOI: https://doi.org/10.1007/3-540-45744-5_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42254-9

  • Online ISBN: 978-3-540-45744-2

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