An Equivalence Net-Condition between Place-Liveness and Transition-Liveness of Petri Nets and Their Initial-Marking-Based Necessary and Sufficient Liveness Conditions

概要

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The structural Necessary and sufficient condition for "the transition-liveness means the place-liveness and vice-versa" of a subclass N_<II> of general Petri nets is given as "the place and transition live Petri net, or PTL net, N^^〜_<II>". Furthermore, "the one-token-condition Petri net, or OTC net, N^^≈_<II>" which means that every MSDL (minimal structural deadlock) is "transition and place live" under at least one initial token, i.e., N^^≈_<II> is "transition and place live" under the above initial marking. These subclasses N_<II>, N^^〜_<II>(⊂N_<II>), and N^^≈_<II>(⊂N^^〜_<II>) are almost the general Petri nets except at least one MSTR (minimal structural trap) and at least one pair of "a virtual MSTR or a virtual STR" and "a virtual MSDL" of an MBTR (minimal behavioral trap) in connection with making an MSDL transition-live.
一般社団法人電子情報通信学会の論文
1994-01-25