Reachability Criterion for Petri Nets with Known Firing Count Vectors

Tadashi MATSUMOTO; Yasushi MIYANO

Reachability Criterion for Petri Nets with Known Firing Count Vectors

Tadashi MATSUMOTO, Yasushi MIYANO

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A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet N_w. This result is based on the decomposition of a given net (N, M_o) with M_d and the concepts of "no immature siphon at the reduced initial marking M_wo" and "no immature trap at the reduced end marking M_wd" on N_w which are both extended from "no token-free siphon at the initial marking M_o" and "no token-free trap at the end marking M_d" on N, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.4 pp.628-634

Publication Date: 1998/04/25

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Type of Manuscript: Special Section LETTER (Special Section on Concurrent Systems Technology)

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Tadashi MATSUMOTO, Yasushi MIYANO, "Reachability Criterion for Petri Nets with Known Firing Count Vectors" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 4, pp. 628-634, April 1998, doi: .
Abstract: A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet N_w. This result is based on the decomposition of a given net (N, M_o) with M_d and the concepts of "no immature siphon at the reduced initial marking M_wo" and "no immature trap at the reduced end marking M_wd" on N_w which are both extended from "no token-free siphon at the initial marking M_o" and "no token-free trap at the end marking M_d" on N, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e81-a_4_628/_p

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@ARTICLE{e81-a_4_628,
author={Tadashi MATSUMOTO, Yasushi MIYANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Reachability Criterion for Petri Nets with Known Firing Count Vectors},
year={1998},
volume={E81-A},
number={4},
pages={628-634},
abstract={A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet N_w. This result is based on the decomposition of a given net (N, M_o) with M_d and the concepts of "no immature siphon at the reduced initial marking M_wo" and "no immature trap at the reduced end marking M_wd" on N_w which are both extended from "no token-free siphon at the initial marking M_o" and "no token-free trap at the end marking M_d" on N, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.},
keywords={},
doi={},
ISSN={},
month={April},}

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TY - JOUR
TI - Reachability Criterion for Petri Nets with Known Firing Count Vectors
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 628
EP - 634
AU - Tadashi MATSUMOTO
AU - Yasushi MIYANO
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 1998
AB - A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet N_w. This result is based on the decomposition of a given net (N, M_o) with M_d and the concepts of "no immature siphon at the reduced initial marking M_wo" and "no immature trap at the reduced end marking M_wd" on N_w which are both extended from "no token-free siphon at the initial marking M_o" and "no token-free trap at the end marking M_d" on N, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.
ER -