Language theory of Petri nets

Abstract

Petri nets where multiple arcs are allows and the capacity of the places need not be bounded are here called Place/Transition systems. The restrictions of the possible finite or infinite occurence sequences of a P/T-system to the transitions are called transition sequences and give the basis to define families of formal languages related to classes of P/T-systems.

We introduce the notation and give a survey on methods and results about sets of finite transition sequences. We will compare the classes of Petri net languages we obtain with other families of languages known from automata and formal language theory. We hope to convince that these techniques and results are useful for the formulation and solution of certain questions about P/T-systems, as well as for comparing the underlying systems.