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.
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Jantzen, M., Zetzsche, G. (2008). Labeled Step Sequences in Petri Nets. In: van Hee, K.M., Valk, R. (eds) Applications and Theory of Petri Nets. PETRI NETS 2008. Lecture Notes in Computer Science, vol 5062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68746-7_19
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DOI: https://doi.org/10.1007/978-3-540-68746-7_19
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