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## An equivalence theorem for labeled marked graphs.

Wolfstahl, Y.;
Yoeli, M.
In:
*IEEE Trans. on Parallel and Distributed Systems, Vol. 5, No. 8*, pages 886-891.
1994.

Abstract:
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 (pi)(S), respectively. In this
paper, we consider an important special case of Petri nets, called labeled
marked graphs. The main result derived in this paper states that if GAMMA1
and GAMMA2 are two structurally deterministic labeled marked graphs, then
(L)(GAMMA1) = L(GAMMA2) double-line arrow pointing left and right
pi(GAMMA1) = pi(GAMMA2).

Keywords:
Petri net languages, Petri nets, labeled marked graphs, structural
determinism.

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