An Equivalence Theorem for Labeled Marked Graphs

  • Authors:
  • Y. Wolfstahl;M. Yoeli

  • Affiliations:
  • -;-

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1994

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Abstract

Petri nets and their languages are a useful model of systems exhibiting concurrentbehavior. The sequential language associated with a given Petri net S consists of allpossible firing sequences of S, where each element of a firing sequence is a singletransition. The concurrent language associated with S consists of all possible concurrentfiring sequences of S, where each element of a concurrent firing sequence is a set oftransitions. The sequential language and the concurrent language associated with S aredenoted by (L)(S) and (/spl pi/)(S), respectively. In this paper, we consider an importantspecial ease of Petri nets, called labeled marked graphs. The main result derived in thispaper states that if /spl Gammasub 1/ and /spl Gammasub 2/ are two structurallydeterministic labeled marked graphs, then (L)(/spl Gammasub 1/)=L(/spl Gammasub 2/)/spl rlhar2spl pi/(/spl Gammasub 1/)=/spl pi/(/spl Gammasub 2/).