Syntax and Semantics of Petri Nets

A uniform presentation of the theories of sequential and distributed computation, using Petri nets as basic model.

Roberto Gorrieri (Author)

9781009613286, Cambridge University Press

Hardback, published 25 September 2025

282 pages
23.5 x 16 x 2 cm, 0.55 kg

Petri nets are one of the most popular tools for modeling distributed systems. This book provides a modern look at the theory behind them, by studying three classes of nets that model (i) sequential systems, (ii) non-communicating parallel systems, and (iii) communicating parallel systems. A decidable and causality respecting behavioral equivalence is presented for each class, followed by a modal logic characterization for each equivalence. The author then introduces a suitable process algebra for the corresponding class of nets and proves that the behavioral equivalence proposed for each class is a congruence for the operator of the corresponding process algebra. Finally, an axiomatization of the behavioral congruence is proposed. The theory is introduced step by step, with ordinary-language explanations and examples provided throughout, to remain accessible to readers without specialized training in concurrency theory or formal logic. Exercises with solutions solidify understanding, and the final chapter hints at extensions of the theory.

1. Introduction
2. Sequential systems
3. Non-communicating parallel systems
4. Communicating systems
5. Other equivalences for Petri nets
6. Conclusion
Appendix. Solutions to selected exercises
Glossary
References
Index.

Subject Areas: Mathematical theory of computation [UYA]