An equivalence theorem for labeled marked graphs
Yaron Wolfstahl, Michael Yoeli · IEEE Transactions on Parallel and Distributed Systems · 1994
Petri nets and their languages are a useful model of systems exhibiting concurrent behavior. The sequential language associated with a given Petri net S consists of all possible firing sequences of S, where each element of a firing sequence is a single transition. The concurrent language associated with S consists of all possible concurrent firing sequences of S, where each element of a concurrent firing sequence is a set of transitions. The sequential language and the concurrent language associated with S are denoted by (L)(S) and (/spl pi/)(S), respectively. In this paper, we consider an important special ease of Petri nets, called labeled marked graphs. The main result derived in this paper states that if /spl Gammasub 1/ and /spl Gammasub 2/ are two structurally deterministic labeled marked graphs, then (L)(/spl Gammasub 1/)=L(/spl Gammasub 2/)/spl rlhar2spl pi/(/spl Gammasub 1/)=/spl pi/(/spl Gammasub 2/).>