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Reviewer: Jan Grabowski

Reisig's Petrinetze, originally published 1982 in German, is now available to English readers. The original edition was improved by including exercises, adding an extensive bibliography with comments, and apparently correcting all faults. The book can be highly recommended as a Petri net primer. Its scope is strongly limited. Reisig covers the very basic notions and most important properties of condition/event systems (Petri nets in the original sense) and place/transition nets (which have been subject to theoretical investigations as a new model of computation). Of the numerous generalization, only two are briefly introduced: predicate/event nets (the tokens of which are individuals of an arbitrary partial algebra) and relational nets (in which the flow relation is a multirelation on a multisorted domain of tokens). This limited choice leaves out esoteric theoretical considerations as well as eclectic practical extensions, but it also sacrifices such an important notion as persistance] The book is distinguished by its strength and objectivity. Reisig avoids overestimating the success of Petri net theory; he stresses the adequacy of the basic concepts to the nature of concurrency, and demonstrates this by well-chosen examples. Moreover, he makes a point of presenting these concepts in a clear, mathematical language with exact definitions and derivations. This makes the book a preferable source for reference and a recommended textbook. What troubles me is that the book contains only a few nontrivial theorems. The most prominent one, Commoner's Liveness Theorem for Free-Choice Nets, is now 13 years old. Many of the challenging structural approaches, such as net morphisms, covering, and decomposition of nets are left out. This is probably not due to conceptual inadequacy, but rather to the lack of results worth presenting. In spite of the growing literature on Petri nets, especially in Western Europe, Reisig's book raises the question of whether 20 years of net theory have fulfilled what Petri's famous invention promised.