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Tadashi MATSUMOTO Ken SAIKUSA Kohkichi TSUJI
Up to now, the only useful and well-known structural or initial-marking-based necessary and sufficient liveness conditions of Petri nets have only been those of an extended free-choice (EFC) net and its subclasses such as a free-choice (FC) net, a forward conflict free (FCF) net, a marked graph (MG), and a state machine (SM). All the above subclasses are activated only by deadlock-trap properties (i.e., real d-t properties in this paper), which mean that every minimal structural deadlock (MSDL ND=(SD, TD, FD, MoD)) in a net contains at least one live minimal structural trap (MSTR NT=(ST, TT, FT, MoT)) which is initially marked. However, the necessary and sufficient liveness conditions for EFCF, EBCF, EMGEFCFEBCF, AC (EFCFC), and the net with kindling traps NKT have recently been determined, in which each MSDL without real d-t properties was also activated by a new type of trap of trap, i.e., behavioral traps (BTRs), which are defined by introducing a virtual MSTR, a virtual maximal structural trap (virtual STR), a virtual MSDL, and a virtual maximal structural deadlock (virtual SDL) into a target MSDL. In this paper, a structural or initial-marking-based necessary and sufficient condition for local liveness (i.e., virtual deadlock-trap properties) of each MSDL ND s.t. SDST, SD
Tadashi MATSUMOTO Shinichi YAMAZAKI
If a general Petri net N = (S, T, F, Mo) is transition-live under Mo, it is evident that each maximal structural deadlock SDL(
Tadashi MATSUMOTO Ken SAIKUSA Shinichi YAMAZAKI
Petri nets are useful in modeling and analyzing various types of discrete-event systems such as parallel processing systems, distributed systems, and sequential control systems, because Petri nets can easily be used to represent such properties of these systems as concurrency, nondecidability, and causality. Various behavioral analytic problems on Petri nets are reduced to reachability and liveness on them. It is also known that the decidability of liveness is equivalent to that of reachability which is solvable. However, useful necessary and sufficient structural liveness conditions have been given only for extended free-choice (EFC) nets and their subclasses. Moreover recently, a necessary and sufficient structural liveness condition for a useful subclass NKT=(SKT, TKT, FKT, MoKT) (i.e., a Petri net in which each minimal structural deadlock (MSDL) contains at least one real or virtual kindling trap, each locally structural-live MSDL ND=(SD, TD, FD, MoD) is never globally dead even if all key transitions for local liveness of each MSDL are controlled by the net of SKT