Diophantine equations, Presburger arithmetic and finite automata

  • Alexandre Boudet
  • Hubert Comon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1059)


We investigate the use of Büchi's techniques for Presburger arithmetic. More precisely, we show how to efficiently compute an automaton which accepts the set of solutions of a linear Diophantine equation (suitably encoded). Following Büchi, this gives a decision technique for the whole Presburger arithmetic. We show however how to compute more efficiently the automaton in the case of disequalities, inequalities and systems of linear Diophantine problems. We also show that such an “automaton algorithm” has a nearly optimal worst case complexity, both for the existential fragment and for the whole first-order theory.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Alexandre Boudet
    • 1
  • Hubert Comon
    • 1
  1. 1.Centre d'OrsayLRI, CNRS URA 410 Bât 490, Université Paris-SudOrsay CedexFrance

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