Presentation	2000/5/25 Some Considerations on Linear-Programming-Based Method for Finding All Elementary Invariants in P/T Petri Nets Tadashi MATSUMOTO, Tomohiro YOSHIDA, Koji TAKASHIMA,
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Abstract(in English)	Invariants in Petri nets are useful for analyzing concurrent systems as well as for evaluating and verifying their performance and specification. Although linear-programming-based method for finding all elementary invariants in P/T nets was proposed about ten years ago, the details of it have not been cleared. In this paper, LP-based formulation (LP1) for Ax=0^, x≥0^ is naturally obtained from Gordon's Theorem for Ax=0^, x≥0^ and M-F Theorem for Ax=b, x≥0^. The necessity for finding non-negative rational solutions under rational-number-operations is also verified. An automatic search method for all extremal points in a polyhedral convex cone is proposed by using the dual problem of LP1.
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Keyword(in English)	P/T Petri nets / elementary invariants / linear programming / finding all extremal points / convex combination
Paper #	CST2000-10
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Committee	CST
Conference Date	2000/5/25(1days)
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Registration To	Concurrent System Technology (CST)
Language	JPN
Title (in Japanese)	(See Japanese page)
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Title (in English)	Some Considerations on Linear-Programming-Based Method for Finding All Elementary Invariants in P/T Petri Nets
Sub Title (in English)
Keyword(1)	P/T Petri nets
Keyword(2)	elementary invariants
Keyword(3)	linear programming
Keyword(4)	finding all extremal points
Keyword(5)	convex combination
1st Author's Name	Tadashi MATSUMOTO
1st Author's Affiliation	Faculty of Engineering, Fukui University()
2nd Author's Name	Tomohiro YOSHIDA
2nd Author's Affiliation	Faculty of Engineering, Fukui University
3rd Author's Name	Koji TAKASHIMA
3rd Author's Affiliation	Faculty of Engineering, Fukui University
Date	2000/5/25
Paper #	CST2000-10
Volume (vol)	vol.100
Number (no)	103
Page	pp.pp.-
#Pages	8
Date of Issue