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1 results

  • On differentiation functions, structure functions, and related languages of context-free grammars

  • Jürgen Dassow, Victor Mitrana, Gheorghe Păun, Ralf Stiebe
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 38 / Issue 3 / July 2004
    Published online by Cambridge University Press:
    15 June 2004, pp. 257-267
    Print publication:
    July 2004

  • We introduce the notion of a differentiation function of acontext-free grammar which gives the number of terminal words that can bederived in a certain number of steps. A grammar is called narrow (ork-narrow) iff its differentiation function is bounded by a constant(by k). We present the basic properties of differentiation functions,especially we relate them to structure function of context-free languagesand narrow grammars to slender languages. We discuss the decidability of the equivalence of grammars with respect to the differentiation function andstructure function and prove the decidability of the k-narrowness of context-free grammars. Furthermore, we introduce languages representing the graph of the differentiation and structure function and relate these languages to those of the Chomsky hierarchy.