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Free-choice Petri nets have been around for more than twenty years, and are a successful branch of net theory. Nearly all the introductory texts on Petri nets devote some pages to them. This book is intended for those who wish to go further. It brings together the classical theorems of free-choice theory obtained by Commoner and Hack in the seventies, and a selection of new results, like the Rank Theorem, which were so far scattered among papers, reports and theses, some of them difficult to access.
Much of the recent research which found its way into the book was funded by the ESPRIT II BRA Action DEMON, and the ESPRIT III Working Group CALIBAN. The book is self-contained, in the sense that no previous knowledge of Petri nets is required. We assume that the reader is familiar with naive set theory and with some elementary notions of graph theory (e.g. path, circuit, strong connectedness) and linear algebra (e.g. linear independence, rank of a matrix). One result of Chapter 4 requires some knowledge of the theory of NP-completeness.
The book can be the subject of an undergraduate course of one semester if the proofs of the most difficult theorems are omitted. If they are included, we suggest the course be restricted to Chapters 1 through 5, which contain most of the classical results on S- and T-systems and free-choice Petri nets. A postgraduate course could cover the whole book.
All chapters are accompanied by a list of exercises. Difficult exercises are marked with asterisks.
Analysis techniques for Petri nets
S-systems and T-systems
Liveness in free-choice systems
The Coverability Theorems
The Rank Theorem
Reduction and synthesis
Home markings
Reachability and shortest sequences
Generalizations