The legal firing sequence problem of Petri nets with state machine structure

The subject of this paper is the legal firing sequence problem (LFS) of Petri nets: given a Petri net PN, an initial marking M and a firing count vector X, find a firing sequence S which starts from M and each transition t appears in /spl delta/ exactly X(t) times as prescribed by X. The results are as follows: (1) LFS is NP-complete even if PN has state machine structure with exactly two kinds of edge weights and X(t)=1 for every transition t; (2) linear time algorithms solving LFS are proposed for several classes of Petri nets having state machine structure.