Journal ArticleDOI
State equation, controllability, and maximal matchings of petri nets
TLDR
This paper discusses Petri nets in the context of the state equation for a linear discrete-time system and shows that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.Abstract:
Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.read more
Citations
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Journal ArticleDOI
Petri nets: Properties, analysis and applications
TL;DR: The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.
Journal ArticleDOI
A Survey of Petri Net Methods for Controlled Discrete EventSystems
TL;DR: An overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets, and two efficient techniques for the on-line computation of the control law.
Journal ArticleDOI
Abstract interpretation
TL;DR: In this paper, the authors propose an interpretative interpretation of the word "interpretation" and "interpretation" in the context of this paper...,..
Journal Article
Linear algebraic and linear programming techniques for the analysis of Place/Transition net systems
TL;DR: The structure theory of transition net systems is surveyed in this paper, mainly from a linear algebraic perspective, and the state equation based analysis of safety properties (e.g., boundedness, mutual exclusion, deadlock-freeness, etc.).
BookDOI
Understanding Petri Nets
TL;DR: This class of processors is important because it can apply analysis techniques like Sand T-invariants to ExSpect specifications only if the specification consists entirely of transitions.
References
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E. Cardoza,R. Lipton,A. R. Meyer +2 more
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Journal ArticleDOI
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