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IEICE TRANSACTIONS on Fundamentals

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

Tadashi MATSUMOTO, Kohkichi TSUJI

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Summary :

The structural necessary and sufficient condition for "the transition-liveness means the place-liveness and vice-versa" of a subclass NII of general Petri nets is given as "the place and transition live Petri net, or PTL net, ÑII". Furthermore, "the one-token-condition Petri net, or OTC net, II" which means that every MSDL (minimal structural deadlock) is "transition and place live" under at least one initial token, i.e., II is "transition and place live" under the above initial marking. These subclasses NII, ÑII( NII), and II(ÑII) 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.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.1 pp.291-301
Publication Date
1994/01/25
Publicized
Online ISSN
DOI
Type of Manuscript
PAPER
Category
Graphs, Networks and Matroids

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