Desel and Esparza’s book is interesting and well-written, and, to the best of my knowledge, it is the most recent and complete reference to free-choice Petri nets available. The topic, free-choice nets (the largest known subset of Petri nets that is computationally tractable), is interesting. The well-balanced mathematical presentation, along with the comments and figures, make it all the more interesting. However, the level of formality makes the text difficult for readers without a specific mathematical background. The book is self-contained, and thus does not require specific knowledge of Petri nets, which are introduced in chapter 2. However, my impression is that some knowledge of Petri nets would greatly increase the benefits of reading this book.
The book is structured well. Ten short chapters identify topics in order of increasing complexity. Each chapter contains a section that delineates the contents of that chapter.
The first three chapters offer the background knowledge necessary to understand the rest of the book. Chapter 1 introduces the basic concepts of Petri nets and free-choice nets. Chapter 2 is an overview of the essential background of Petri nets. Chapter 3 describes S-systems and T-systems, a proper subset of free-choice nets. S- and T-systems are used to introduce important theorems that are later generalized for free-choice nets.
The last seven chapters deal with free-choice nets. Chapter 4 introduces siphons and traps, which are used to formulate and demonstrate the commoner’s theorem. Chapter 5 demonstrates the S-coverability and T-coverability theorems, which present a relationship between free-choice nets and the S- and T-systems. Chapter 6 demonstrates the rank theorem, which characterizes free-choice nets that admit live and bounded markings. Chapter 7 describes a constructive technique that identifies live and bounded free-choice nets or indicates the components of the net that do not imply liveness or boundedness. Chapter 8 deals with home markings of live and bounded free-choice nets, and provides a polynomial algorithm that decides whether a reachable marking is a home marking. Chapter 9 deals with live and bounded free-choice nets that are cyclic. Chapter 10 weakens the commoner’s and rank theorems to address a wider subclass of Petri nets.
The chapters are strongly interrelated, so a selected reading of them is almost impossible. Each chapter includes exercises that help the reader practice the concepts introduced in the chapter, and bibliographic notes offer additional reading material. The references cover related topics well.
The book is also structured well for courses on free-choice nets. The preface states that the first five chapters are appropriate for undergraduate classes, while the authors claim that the entire book can be used for postgraduate courses. This book is not an introductory text on Petri nets, however, nor would it complement a general text in an introductory course. Only students with a strong mathematical background and a good knowledge of Petri nets can really benefit from a course on free-choice nets based on this book.
Although I do not like the general presentation of this series, which tends to cram too much on to each page, the typographical presentation of this book is very good: definitions, theorems, and proofs are identified easily. I did not notice any annoying typos, and the numerous formulas are clearly written, while the graphics are clean and well-positioned.
I would definitely recommend this book to anyone who is studying free-choice nets. They will discover a good overview of all the important results in the field over the past 20 years. I also recommend this book to researchers and practitioners interested in Petri nets, since they will probably increase their knowledge of this topic.
