Petri Nets and Discrete Events Systems

Petri Nets and Discrete Events Systems

Juan L. G. Guirao, Fernando L. Pelayo
Copyright: © 2013 |Pages: 10
DOI: 10.4018/978-1-4666-2651-5.ch016
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Abstract

This paper provides an overview over the relationship between Petri Nets and Discrete Event Systems as they have been proved as key factors in the cognitive processes of perception and memorization. In this sense, different aspects of encoding Petri Nets as Discrete Dynamical Systems that try to advance not only in the problem of reachability but also in the one of describing the periodicity of markings and their similarity, are revised. It is also provided a metric for the case of Non-bounded Petri Nets.
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Petri Nets Modeling Discrete-Events Processes

A Petri Net is a bipartite graph constituted by two kinds of nodes, namely, places and transitions that alternate on a path made up of consecutive arcs. Places are usually represented by circles and transitions by boxes or rectangles. The number of places is finite and not zero and the same occurs for the number of transitions (David, 1994). More rigorously:

  • Definition 1: A Petri Net (PN) is a triple 978-1-4666-2651-5.ch016.m01 consisting of two finite sets 978-1-4666-2651-5.ch016.m02 and 978-1-4666-2651-5.ch016.m03, and a relation 978-1-4666-2651-5.ch016.m04 defined over 978-1-4666-2651-5.ch016.m05, such that:

  • 1.

    978-1-4666-2651-5.ch016.m06

  • 2. 978-1-4666-2651-5.ch016.m07

  • 3.

    978-1-4666-2651-5.ch016.m08

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