Presentation	2001/11/19 A New Algorithm to Derive Generators for Both Invariants and Particular Solutions of State Equation for a P/T Petri Net : Extended Fourier-Motzkin Method Maki TAKATA, Tadashi MATSUMOTO, Seiichiro MORO,
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Abstract(in English)	A nonnegative integer inhomogeneous solution x⋴Z^_ of state equation Ax=b of a P/T Petri net system means the firing count vector of transitions. Both generators of a homogeneous solution and a particular solution are necessary for analyzing reachability problems. Generator of a solution is divided into six levels according to the complexity of the calculation. It is difficult to obtain directly nonnegative integer basic particular solutions at level 4 from an algorithmic point of view. However, it is easy to choose nonnegative integer basic particular solutions at level 4 from nonnegative integer particular solutions at level 6. Therefore, the purpose of this paper is to obtain the level 6 generator of a solution. There exist some indirect methods which obtain the level 6 generator through the lower one. However, there is no method to find directly the level 6 generator from the incidence matrix A. Then, we paid attention to the Fourier-Motzkin method which calculates the family of T-invariants including all of minimal support T-invariants of Ax=0^. The first, we improve the FM method to obtain all of minimal T-invariants of Ax=0. Next, we apply the improved FM method to the augmented system with incidence matrix A^^～=[A, -b]⋴Z^. All of minimal T-invariants of A^^～x^^～=0^ include all of minimal T-invariants and all of nonnegative integer particular solutions at level 6 of Ax=b.
Keyword(in Japanese)	(See Japanese page)
Keyword(in English)	P/T Petri nets / state equations / T-invariants / particular solutions / generators / Fourier-Motzkin method
Paper #	CAS2001-65,CST2001-18
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Committee	CAS
Conference Date	2001/11/19(1days)
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Registration To	Circuits and Systems (CAS)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	A New Algorithm to Derive Generators for Both Invariants and Particular Solutions of State Equation for a P/T Petri Net : Extended Fourier-Motzkin Method
Sub Title (in English)
Keyword(1)	P/T Petri nets
Keyword(2)	state equations
Keyword(3)	T-invariants
Keyword(4)	particular solutions
Keyword(5)	generators
Keyword(6)	Fourier-Motzkin method
1st Author's Name	Maki TAKATA
1st Author's Affiliation	Department of Electrical and Electronics Engineering, Faculty of Engineering, Fukui University()
2nd Author's Name	Tadashi MATSUMOTO
2nd Author's Affiliation	Department of Electrical and Electronics Engineering, Faculty of Engineering, Fukui University
3rd Author's Name	Seiichiro MORO
3rd Author's Affiliation	Department of Electrical and Electronics Engineering, Faculty of Engineering, Fukui University
Date	2001/11/19
Paper #	CAS2001-65,CST2001-18
Volume (vol)	vol.101
Number (no)	458
Page	pp.pp.-
#Pages	8
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