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How to Compose Presburger-Accelerations: Applications to Broadcast Protocols

  • Alain Finkel
  • Jérôme Leroux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2556)

Abstract

Finite linear systems are finite sets of linear functions whose guards are defined by Presburger formulas, and whose the squares matrices associated generate a finite multiplicative monoid. We prove that for finite linear systems, the accelerations of sequences of transitions always produce an effective Presburger-definable relation. We then show how to choose the good sequences of length n whose number is polynomial in n although the total number of sequences of length n is exponential in n. We implement these theoretical results in the tool FAST [FAS] (Fast Acceleration of Symbolic Transition systems). FAST computes in few seconds the minimal deterministic finite automata that represent the reachability sets of 8 well-known broadcast protocols.

Keywords

Presburger model checking verification infinite-state systems reachability set acceleration 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alain Finkel
    • 1
  • Jérôme Leroux
    • 1
  1. 1.Laboratoire Spécification et VérificationCNRS UMR 8643 amp; ENS de CachanCachan cedexFrance

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