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Matsumoto, Tadashi 대한전자공학회 1996 APCCAS:Asia Pacific Conference on Circuits And Sys Vol.1 No.1
Petri nets are useful in modeling concurrent/parallel systems. But, their applications to practice have been slow due to lack of computational tools and techniques capable of dealing with large scale nets. In this paper, first, optimal-control-based analysis aspect of the sub-marking reachability problems (SMR) included the wellknown reachability problems (MR) and MR with a firing count vector (MR-FV) is discussed and a semi-polynomial time algorithm for SMR ⊃ MR is shown by applying the discrete-time Pontryagin's minimum principle (PMP) which includes the linear programming (LP) for each sub-problem optimization, where the checking procedure for critical siphons at each time, however, is neglected in the above time-complexity evaluation. Secondly, it is shown that the reachability problems and their inverse problems with no intermediate marking constraints, including the generalized submarking problems (GSMR) and the generalized submarking reachability on a minimum initial marking (MIS), are classified into five problems as in Table 1. Thirdly, it is briefly discussed that other three problems with an unknown firing count vector can be reduced to SMR ⊃ MR.