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

Jürgen Dassow; Victor Mitrana; Gheorghe Păun; Ralf Stiebe

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 38, Issue: 3, page 257-267
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Dassow, Jürgen, et al. "On differentiation functions, structure functions, and related languages of context-free grammars." RAIRO - Theoretical Informatics and Applications 38.3 (2010): 257-267. <http://eudml.org/doc/92742>.

@article{Dassow2010,
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. },
author = {Dassow, Jürgen, Mitrana, Victor, Păun, Gheorghe, Stiebe, Ralf},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Differentiation function; structure function; slender languages; narrow grammars},
language = {eng},
month = {3},
number = {3},
pages = {257-267},
publisher = {EDP Sciences},
title = {On differentiation functions, structure functions, and related languages of context-free grammars},
url = {http://eudml.org/doc/92742},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Dassow, Jürgen
AU - Mitrana, Victor
AU - Păun, Gheorghe
AU - Stiebe, Ralf
TI - On differentiation functions, structure functions, and related languages of context-free grammars
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 3
SP - 257
EP - 267
AB - 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.
LA - eng
KW - Differentiation function; structure function; slender languages; narrow grammars
UR - http://eudml.org/doc/92742
ER -

References

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  14. M. Latteux and G. Thierrin, Semidiscrete context-free languages. Internat. J. Comput. Math.14 (1983) 3–18.  
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