Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems of time Petri nets. In this model, a minimal and a maximal firing delays are assigned to each transition. If a transition is 'enabled' it can fire after minimal delay has passed and must fire before maximal delay has elapsed. Since time Petri net can simulate register machines, it has equivalent modeling power to that of Turing machine. It means, however, that most of the analysis problems of time Petri nets with general net structures are undecidable. In this paper, net structures are restricted to a subclass called partially ordered condition (POC) nets and dissynchronous choice (DC) nets. Firing delays are also restricted to satisfy 'static fair condition' which assures chance to fire for all transitions enabled simultaneously. First, a sufficient condition of liveness of time POC net with the static fair condition is derived. Then it is shown that liveness of time DC net with static fair condition is equivalent to liveness of the underlying nontime net. This means that liveness problem of this class is decidable. Lastly, liveness problem of extended free choice (EFC) net is shown to be decidable.
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Atsushi OHTA, Tomiji HISAMURA, "On Liveness of Time POC Nets with the Static Fair Condition" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 8, pp. 1648-1655, August 1999, doi: .
Abstract: Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems of time Petri nets. In this model, a minimal and a maximal firing delays are assigned to each transition. If a transition is 'enabled' it can fire after minimal delay has passed and must fire before maximal delay has elapsed. Since time Petri net can simulate register machines, it has equivalent modeling power to that of Turing machine. It means, however, that most of the analysis problems of time Petri nets with general net structures are undecidable. In this paper, net structures are restricted to a subclass called partially ordered condition (POC) nets and dissynchronous choice (DC) nets. Firing delays are also restricted to satisfy 'static fair condition' which assures chance to fire for all transitions enabled simultaneously. First, a sufficient condition of liveness of time POC net with the static fair condition is derived. Then it is shown that liveness of time DC net with static fair condition is equivalent to liveness of the underlying nontime net. This means that liveness problem of this class is decidable. Lastly, liveness problem of extended free choice (EFC) net is shown to be decidable.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_8_1648/_p
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@ARTICLE{e82-a_8_1648,
author={Atsushi OHTA, Tomiji HISAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Liveness of Time POC Nets with the Static Fair Condition},
year={1999},
volume={E82-A},
number={8},
pages={1648-1655},
abstract={Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems of time Petri nets. In this model, a minimal and a maximal firing delays are assigned to each transition. If a transition is 'enabled' it can fire after minimal delay has passed and must fire before maximal delay has elapsed. Since time Petri net can simulate register machines, it has equivalent modeling power to that of Turing machine. It means, however, that most of the analysis problems of time Petri nets with general net structures are undecidable. In this paper, net structures are restricted to a subclass called partially ordered condition (POC) nets and dissynchronous choice (DC) nets. Firing delays are also restricted to satisfy 'static fair condition' which assures chance to fire for all transitions enabled simultaneously. First, a sufficient condition of liveness of time POC net with the static fair condition is derived. Then it is shown that liveness of time DC net with static fair condition is equivalent to liveness of the underlying nontime net. This means that liveness problem of this class is decidable. Lastly, liveness problem of extended free choice (EFC) net is shown to be decidable.},
keywords={},
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ISSN={},
month={August},}
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TY - JOUR
TI - On Liveness of Time POC Nets with the Static Fair Condition
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1648
EP - 1655
AU - Atsushi OHTA
AU - Tomiji HISAMURA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1999
AB - Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems of time Petri nets. In this model, a minimal and a maximal firing delays are assigned to each transition. If a transition is 'enabled' it can fire after minimal delay has passed and must fire before maximal delay has elapsed. Since time Petri net can simulate register machines, it has equivalent modeling power to that of Turing machine. It means, however, that most of the analysis problems of time Petri nets with general net structures are undecidable. In this paper, net structures are restricted to a subclass called partially ordered condition (POC) nets and dissynchronous choice (DC) nets. Firing delays are also restricted to satisfy 'static fair condition' which assures chance to fire for all transitions enabled simultaneously. First, a sufficient condition of liveness of time POC net with the static fair condition is derived. Then it is shown that liveness of time DC net with static fair condition is equivalent to liveness of the underlying nontime net. This means that liveness problem of this class is decidable. Lastly, liveness problem of extended free choice (EFC) net is shown to be decidable.
ER -