DocumentCode :
3057750
Title :
Free-choice Petri nets: the algebraic approach
Author :
Baccelli, F. ; Foss, S. ; Gaujal, B.
Author_Institution :
Inst. Nat. de Recherche en Inf. et Autom., Sophia Antipolis, France
Volume :
2
fYear :
1995
fDate :
13-15 Dec 1995
Firstpage :
2023
Abstract :
In this paper, we show how a decomposition of a free choice Petri net into a `routing´ network and marked graph subnetworks (i.e. linear subnetworks in the [max,+] setting) leads to new methods and algorithms to test structural as well as temporal properties of the net. We show how this decomposition allows one to: (in the timed case) establish evolution equations which involve two linear systems, a (min,+)-linear system, and a quasi (+,×)-linear one; (in the stochastic case) check stability i.e. the fact that the marking remains bounded in probability. The main tools for proving these properties are graph theory, idempotent algebras and ergodic theory
Keywords :
Petri nets; algebra; (min,+)-linear system; algebraic approach; ergodic theory; evolution equations; free-choice Petri net decomposition; graph theory; idempotent algebras; linear subnetworks; marked graph subnetworks; probability-bounded marking; quasi (+,×)-linear system; routing network; stability; structural properties; temporal properties; Algebra; Equations; Graph theory; Linear systems; Petri nets; Routing; Stability; Stochastic processes; Stochastic systems; Testing;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
ISSN :
0191-2216
Print_ISBN :
0-7803-2685-7
Type :
conf
DOI :
10.1109/CDC.1995.480645
Filename :
480645
Link To Document :
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