Subset Languages of Petri Nets Part I: The Relationship to String Languages and Normal Forms

Abstract In this paper we are interested in language theoretical properties of Petri nets. However, in this research we consider a step to consist of concurrent firing of a set of transitions. In this way a firing sequence will be a sequence of subsets of the set of all transitions. The set of all such subset firing sequences (or the set of all those subset firing sequences that lead to one of the finite number of final markings) forms the subset language of a given net (to consider such a set to be a language one has to consider subsets to be letters of the alphabet used to record behaviour of nets). The aim of the paper is to present a systematic research exploring the above point of view. First of all we point out several differences between the standard ‘string language’ approach and the ‘subset language’ approach. Then we proceed to the investigation of properties of Petri nets as generators of subset languages. We provide here some normal form results (and notice that those results and their proofs are quite different from the case when one considers Petri nets as generators of string languages).