Analysis of Petri Nets by Ordering Relations in Reduced Unfoldings

  • Authors:
  • Alex Kondratyev;Michael Kishinevsky;Alexander Taubin;Sergei Ten

  • Affiliations:
  • The University of Aizu, Aizu-Wakamatsu, 965-80, Japan.;The University of Aizu, Aizu-Wakamatsu, 965-80, Japan.;The University of Aizu, Aizu-Wakamatsu, 965-80, Japan.;The University of Aizu, Aizu-Wakamatsu, 965-80, Japan.

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 1998

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Abstract

This paper suggests a way for Petri Net analysis by checkingthe ordering relations between places and transitions. The method isbased on unfolding the original net into an equivalent acyclicdescription. We improved on the previously known cutoff criterionfor truncating unfoldings [13]. No restrictions are imposed on theclass of general PNs. The new criterion significantly reduces thesize of an unfolding obtained by a PN. The properties of PNs foranalysis can be various: boundedness, safety, persistency etc. Apractical example of the suggested approach is given in an applicationto asynchronous design. Circuit behavior is specified by aninterpreted Petri net, called a Signal Transition Graph (STG) which isthen analyzed for implementability by an asynchronous hazard-freecircuit. The implementability conditions are formulated in such a waythat they can be checked by analysis of ordering relations betweensignal transitions rather than by traversal of states. This allows usto avoid the state explosion problem for highly parallelspecifications. The experimental results show that for highlyparallel STGs checking their implementability by an unfolding is oneto two orders of magnitude less time-consuming than checking it bysymbolic BDD traversal of the corresponding State Graph.