Erasing in Petri Net Languages and Matrix Grammars

Authors:
Georg Zetzsche
Affiliations:
MIN-Faculty, Department Informatik, Universität Hamburg, Hamburg, 22527
Venue:
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Year:
2009

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Abstract

It is shown that applying linear erasing to a Petri net language yields a language generated by a non-erasing matrix grammar. The proof uses Petri net controlled grammars. These are context-free grammars, where the application of productions has to comply with a firing sequence in a Petri net. Petri net controlled grammars are equivalent to arbitrary matrix grammars (without appearance checking), but a certain restriction on them (linear Petri net controlled grammars) leads to the class of languages generated by non-erasing matrix grammars.It is also shown that in Petri net controlled grammars (with final markings and arbitrary labeling), erasing rules can be eliminated, which yields a reformulation of the problem of whether erasing rules in matrix grammars can be eliminated.