Labeled Step Sequences in Petri Nets

Authors:
Matthias Jantzen;Georg Zetzsche
Affiliations:
Faculty of Mathematics, Informatics, and Natural Sciences, Deptartment of Informatics, University of Hamburg, Hamburg 22527;Faculty of Mathematics, Informatics, and Natural Sciences, Deptartment of Informatics, University of Hamburg, Hamburg 22527
Venue:
PETRI NETS '08 Proceedings of the 29th international conference on Applications and Theory of Petri Nets
Year:
2008

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Abstract

We compare various modes of firing transitions in Petri nets and investigate classes of languages specified by them. We define languages through steps, (i. e., sets of transitions), maximal steps, multi-steps, (i. e., multisets of transitions), and maximal multi-steps of transitions in Petri nets. However, by considering labeled transitions, we do this in a different manner than in [Burk 81a, Burk 83]. Namely, we allow only sets and multisets of transitions to form a (multi-)step, if they all share the same label. In a sequence of (multi-)steps, each of them contributes its label once to the generated word. Through different firing modes that allow multiple use of transitions in a single multi-step, we obtain a hierarchy of families of languages. Except for the maximal multi-steps all classes can be simulated by sequential firing of transitions.