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An Equivalence Theorem for Labeled Marked Graphs
August 1994 (vol. 5 no. 8)
pp. 886-891

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/).

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Index Terms:
Index TermsPetri nets; formal languages; multiprocessing systems; equivalence theorem; labeledmarked graphs; Petri nets; structural determinism; sequential language; firing sequences;transitions; concurrent language
Y. Wolfstahl, M. Yoeli, "An Equivalence Theorem for Labeled Marked Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 8, pp. 886-891, Aug. 1994, doi:10.1109/71.298217
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