# 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 - Informatique Théorique et Applications (2004)

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

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topDassow, Jürgen, et al. "On differentiation functions, structure functions, and related languages of context-free grammars." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 38.3 (2004): 257-267. <http://eudml.org/doc/245023>.

@article{Dassow2004,

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 - Informatique Théorique et Applications},

keywords = {differentiation function; structure function; slender languages; narrow grammars},

language = {eng},

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/245023},

volume = {38},

year = {2004},

}

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 - Informatique Théorique et Applications

PY - 2004

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/245023

ER -

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