All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.1 pp.399-404
- Publication Date
- 2005/01/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietfec/e88-a.1.399
- Type of Manuscript
- LETTER
- Category
- Concurrent Systems
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Akira MURAYA, Tadashi MATSUMOTO, Seiichiro MORO, Haruo HASEGAWA, "All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets" in IEICE TRANSACTIONS on Fundamentals,
vol. E88-A, no. 1, pp. 399-404, January 2005, doi: 10.1093/ietfec/e88-a.1.399.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.1.399/_p
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@ARTICLE{e88-a_1_399,
author={Akira MURAYA, Tadashi MATSUMOTO, Seiichiro MORO, Haruo HASEGAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets},
year={2005},
volume={E88-A},
number={1},
pages={399-404},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e88-a.1.399},
ISSN={},
month={January},}
Copy
TY - JOUR
TI - All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 399
EP - 404
AU - Akira MURAYA
AU - Tadashi MATSUMOTO
AU - Seiichiro MORO
AU - Haruo HASEGAWA
PY - 2005
DO - 10.1093/ietfec/e88-a.1.399
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2005
AB - 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.
ER -
English
