By René David

This monograph provides a good written and obviously geared up advent within the commonplace equipment of discrete, non-stop and hybrid Petri Nets. ranging from the fundamentals of Petri nets the publication imparts a correct knowing of continuing and hybrid Petri Nets. holding the consistency of simple techniques through the textual content it introduces a unified framework for all of the types provided. The ebook is a systematic monograph in addition to a didactic instructional that's effortless to appreciate because of many workouts with suggestions, precise figures and a number of other case reviews. It demonstrates that Petri nets are a deep, functional and alive box very important for researchers, engineers and graduate scholars in engineering and laptop science.

Improvements and additions during this moment variation have largely benefited from instructing, scholar questions, and diverse discussions with colleagues or occupied with the topic.

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**Additional resources for Discrete, Continuous, and Hybrid Petri Nets**

**Example text**

2 A PN is said to be safe for an initial marking m 0 if for all reachable markings, each place contains zero or one token. 3 (a) Bounded PN. (b) Unbounded PN. m3 P1 T1 P2 m2 m3 Properties of Petri Nets 25 A safe PN is thus a particular case of bounded Petri net for which all the places are 1-bounded. 3a is bounded but not safe. 2 is safe. As a matter of fact we can see that for each of the reachable markings, there is always zero or one token in each place. 1 The properties of safe and bounded PNs depend on the initial marking m0.

Equal conflict PNs were introduced in [TeSi93] and widely studied in [TeSi 96]. A technique allowing the conversion of an impure PN into a pure PN can be found in [Br 83] or [DaAl 89&92] . The model of colored PNs introduced by K. Jensen [Je 81] is widely used; parts of [Al 87] and [DaAl 89&92] are devoted to this model. Predicate Petri nets are also an interesting kind of colored PNs [GeLa 79]. The concepts of hierarchy and high-level nets are associated with the colored PNs [Si 85][HuJeSh 89] [MaMuSi87][JeRo 91].

4 Extended Petri Nets An extended Petri net contains special arcs qualified as inhibitor. An inhibitor arc is a directed arc which leaves a place Pi to reach a transition T j . 10. In this figure, the inhibitor arc between P2 and T 1 means that transition T 1 is only enabled if place P2 does not contain any tokens. Firing consists in removing a token from each input place of T 1, with the exception of P2, and in adding a token to each output place of T1. 10a, transition T 1 is not enabled because P1 does not contain any tokens.