Leftist grammars and the chomsky hierarchy

  • Authors:
  • Tomasz Jurdziński;Krzysztof Loryś

  • Affiliations:
  • Institute of Computer Science, Wrocław University, Wrocław, Poland;Institute of Computer Science, Wrocław University, Wrocław, Poland

  • Venue:
  • FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
  • Year:
  • 2005

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Abstract

Leftist grammars can be characterized in terms of rules of the form a→ ba and cd→ d, without distinction between terminals and nonterminals. They were introduced by Motwani et. al. [9] , where the accessibility problem for some general protection system was related to the membership problem of these grammars. This protection system was originally proposed in [3,10] in the context of Java virtual worlds. We show that the set of languages defined by general leftist grammars is not included in CFL, answering in negative a question from [9]. Moreover, we relate some restricted but naturally defined variants of leftist grammars to the language classes of the Chomsky hierarchy.