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

Published online by Cambridge University Press:  15 June 2004

Jürgen Dassow ,
Victor Mitrana ,
Gheorghe Păun  and
Ralf Stiebe
Jürgen Dassow
Affiliation:
Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, PSF 4120, 39016 Magdeburg, Germany; [email protected].; [email protected].
Victor Mitrana
Affiliation:
University of Bucharest, Institute of Mathematics, Str. Academiei 14, 70109 Bucuresti, Romania. Rovira i Virgili University, Research Group in Mathematical Linguistics, Pça. Imperial Tarraco 1, 43005, Tarragona, Spain; [email protected].
Gheorghe Păun
Affiliation:
Institute of Mathematics of the Romanian Academy, PO Box 1–764, 70700 Bucuresti, Romania; [email protected].
Ralf Stiebe
Affiliation:
Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, PSF 4120, 39016 Magdeburg, Germany; [email protected].; [email protected].
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Abstract

We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. A grammar is called narrow (or k-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 languages and narrow grammars to slender languages. We discuss the decidability of the equivalence of grammars with respect to the differentiation function and structure 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.

Keywords

Differentiation functionstructure functionslender languages
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 3 , July 2004 , pp. 257 - 267
Copyright
© EDP Sciences, 2004

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