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All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets
Akira MURAYA
Tadashi MATSUMOTO
Seiichiro MORO
Haruo HASEGAWA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E88-A No.1 pp.399-404
Publication Date: 2005/01/01
Online ISSN:
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Concurrent Systems
Keyword:
P/T Petri nets,
firing count vectors,
fundamental/minimal particular solutions,
minimal T-invariants,
state equation,
Full Text: PDF(270.4KB)
Summary:
For fixed initial and destination states (i.e., markings), M0 and Md, there exist generally infinite firing count vectors in a Petri net. In this letter, it is shown that all fundamental particular solutions as well as all minimal T-invariants w.r.t. firing count vectors are needed to express an arbitrary firing count vector for the fixed M0 and Md. An algorithm for finding a special firing count vector which is expressed by using the only one specified fundamental particular solution is also given.
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