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Petri Nets

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Abstract

An alternative to automata for untimed models of DES is provided by Petri nets. These models were first developed by C. A. Petri in the early 1960s. As we will see, Petri nets are related to automata in the sense that they also explicitly represent the transition function of DES. Like an automaton, a Petri net is a device that manipulates events according to certain rules. One of its features is that it includes explicit conditions under which an event can be enabled; this allows the representation of very general DES whose operation depends on potentially complex control schemes. This representation is conveniently described graphically, at least for small systems, resulting in Petri net graphs; Petri net graphs are intuitive and capture a lot of structural information about the system.

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Notes

  1. 1.

    This explains the use of the word “attempting” in the preceding sentence.

  2. 2.

    This section assumes that the reader is familiar with the material presented in Chap. 3, principally Sects. 3.2, 3.4, and 3.5.

  3. 3.

    This section is included for readers interested in the connection between the results of Chap. 3 and Petri nets. Its material is more specialized than that in the rest of this chapter and it may be skipped without loss of continuity.

  4. 4.

    An alternative is to use an inhibitor arc – see the references listed at the end of the chapter – but this is undesirable as Petri nets with inhibitor arcs are not tractable analytically.

  5. 5.

    The term “monitor” is also used in the literature to describe control places.

  6. 6.

    See the books by Moody & Antsaklis and Iordache & Antsaklis for a detailed treatment of this theory.

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Correspondence to Christos G. Cassandras .

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Cassandras, C.G., Lafortune, S. (2021). Petri Nets. In: Introduction to Discrete Event Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-72274-6_4

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  • DOI: https://doi.org/10.1007/978-3-030-72274-6_4

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  • Publisher Name: Springer, Cham

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