Petri Net Languages and One-Sided Dyck-Reductions On Context-Free Sets

  • M. Jantzen
  • H. Petersen


In [2, 6, 8, 9] cancellation grammars (or grammars related to them) are defined and their relation to well-known families of languages are studied. Savitch showed in [9] that the class of EOL languages can be obtained from the context-free sets (CF) by iteratively and completely cancelling one matching pair xx̄ of parenthesis x and x̄. This type of reduction is here called a Dyck1-reduction on a set L which can be taken from any family of languages — not only the context-free sets — and thus need not be definable by certain restricted classes of grammars as in [2, 9]. In this short note we will show that we get all (free) terminal Petri net languages and all transition sequences from the context-free sets by Dyck1-reductions and, moreover, each non-erasing homomorphic image thereof, the corresponding families denoted by L and P as in [7].




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Book, M. Jantzen, C. Wrathall: Monadic Thue Systems, Theoret. Comput. Sci, 19(1982) 231–251.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    V. Geffert: Grammars with context dependency restricted to synchronization, Proc. MFCS 86, Lecture Notes in Comput. Sci. 233, Springer-Verlag (1986) 370–378.Google Scholar
  3. [3]
    S.A. Greibach: Full AFL’s and nested iterated substitution, Information and Control, 16(1970) 7–35.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    M. Jantzen: Language theory of Petri nets, Proc. Advanced Course on Petri Nets, Bad Honnef (1986), to appear 1987.Google Scholar
  5. [5]
    J. van Leeuwen: A generalization of Parikh’s theorem in formal language theory, Proc. ICALP 74, Lecture Notes in Comput. Sci. 14, Springer-Verlag (1974) 17–26.Google Scholar
  6. [6]
    H. Petersen: Klammer-Löschungs-Grammatiken und Dyckreduktionen auf kontextfreien Sprachen, Stuäienarbeit am FB Informatik, Univ. Hamburg (1986).Google Scholar
  7. [7]
    J.L. Peterson: Petri Net Theory and the Modeling of Systems, Prentice Hall (1981).Google Scholar
  8. [8]
    B. Rovan: A framework for studying grammars, Proc. MFCS 81, Lecture Notes in Comput. Sci. 118, Springer-Verlag (1981) 473–482.Google Scholar
  9. [9]
    W.J. Savitch: Parantheses grammars and Lindenmayer systems, in: G. Rozenberg, A. Salomaa (eds), The Book of L, Sprinaer-Verlag (1986) 403–411.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • M. Jantzen
    • 1
  • H. Petersen
    • 1
  1. 1.FB InformatikUniversität HamburgGermany

Personalised recommendations