A survey of siphons in Petri nets

Petri nets have gained increasing usage and acceptance as a basic model of asynchronous concurrent systems since 1962. As a class of structural objects of Petri nets, siphons play a critical role in the analysis and control of systems modeled with Petri nets. This paper surveys the state-of-the-art siphon theory of Petri nets including basic concepts, computation of siphons, controllability conditions, and deadlock control policies based on siphons. Some open problems on siphons are discussed, such as the maximally permissive supervisor design problems based on siphons and the application of siphons to robust supervisory control. This survey is expected to serve as a reference source for the growing number of Petri net researchers and practitioners.