Necessary conditions for subclasses of random context languages

  • Authors:

  • Sigrid Ewert;Andries Van Der Walt

  • Affiliations:

  • School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa;Department of Mathematical Sciences, Computer Science Division, University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

Random context grammars belong to the class of context-free grammars with regulated rewriting. Their productions depend on context that may be randomly distributed in a sentential form. Context is classified as either permitting or forbidding, where permitting context enables the application of a production and forbidding context inhibits it. We have proven a pumping lemma for random permitting context languages and a shrinking lemma for random forbidding context languages. We now present new necessary conditions for both these classes of languages and illustrate them with examples. We also present and illustrate a new necessary condition for context-free languages.