Normal Petri nets
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It is shown that the reachability set of a marked Petri net is an effectively computable semilinear set unless the total number of tokens in a minimal circuit is decreased to 0.About:
This article is published in Theoretical Computer Science.The article was published on 1984-01-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Stochastic Petri net & Petri net.read more
Citations
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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.
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A unified approach for deciding the existence of certain Petri net paths
TL;DR: A unified approach for deriving complexity results for a number of Petri net problems is developed, first defining a class of formulas for paths in Petri nets, and showing that the satisfiability problem for these formulas is EXPSPACE complete.
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A Class of Petri Nets That a Necessary and Sufficient Condition for Reachability is Obtainable
TL;DR: Several new classes of Petri nets are defined by structural conditions related to directed circuits, where a necessary and sufficient condition for reachability is obtained for trap circuit Petrinets (TC nets), where a Petri net is called a TC net if the set of places on any directed circuit forms a trap.
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Normal and sinkless Petri nets
TL;DR: This work gives the first comprehensive complexity analysis of a class of potentially unbounded Petri nets defined in terms of their behavior, and argues that although neither normal nor sinkless Petrinets are strictly more powerful than persistentPetri nets, they nonetheless are both capable of modeling a more interesting class of problems.
References
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Marked directed graphs
TL;DR: A problem of maximal storage requirements for a simple flowchart model called the Marked Graph Model, which permits algorithnfic answers to problems which in their model were quite complex to solve, e.g., the termination problem.
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Semigroups, Presburger formulas, and languages.
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On the Reachability Problem for 5-Dimensional Vector Addition Systems
TL;DR: The reachability set for vector addition systems of dimension less than or equal to five are shown to be effectively computable semilinear sets, and reachability, equvalence and containment are decidable up to dimension 5.
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Properties of Conflict-Free and Persistent Petri Nets
TL;DR: This paper investigates two unportant special types of Petn nets, the conflict-free nets and the persistent nets, with the former being a proper subset of the latter.
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The equality problem for vector addition systems is undecidable
TL;DR: The usefulness of Petri nets for treating problems about vector addition systems is demonstrated by giving a simple exposition of Rabin's proof of the undecidability of the inclusion problem for vector addition system reachability sets.