Erasing in Petri Net Languages and Matrix Grammars

  • Georg Zetzsche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5583)


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.


Empty Word Language Class Sentential Form Reachability Problem Terminal Symbol 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Georg Zetzsche
    • 1
  1. 1.MIN-Faculty, Department InformatikUniversität HamburgHamburgGermany

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