An automata-theoretic approach to Presburger arithmetic constraints

Extended abstract
  • Pierre Wolper
  • Bernard Boigelot
Invited Talks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 983)


This paper introduces a finite-automata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance all usual operations on sets of integer vectors translate naturally to operations on automata. Second, the use of concurrent automata makes it compact. Third, it is insensitive to the representation size of integers. Our representation can be used whenever arithmetic constraints are needed. To illustrate its possibilities we show that it can handle integer programming optimally, and that it leads to a new original algorithm for the satisfiability of arithmetic inequalities.


Finite Automaton Integer Programming Problem Integer Vector Number Component Quantify Boolean Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Pierre Wolper
    • 1
  • Bernard Boigelot
    • 1
  1. 1.Institut Montefiore B28Université de LiègeLiège Sart TilmanBelgium

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