Extending regular expressions with homomorphic replacement

Henning Bordihn; Jürgen Dassow; Markus Holzer

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 2, page 229-255
  • ISSN: 0988-3754

Abstract

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We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns, pattern expressions, H-systems and uniform substitutions are also investigated. Furthermore, we present their closure properties with respect to TRIO operations and discuss the decidability status and complexity of fixed and general membership, emptiness, and the equivalence problem.

How to cite

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Bordihn, Henning, Dassow, Jürgen, and Holzer, Markus. "Extending regular expressions with homomorphic replacement." RAIRO - Theoretical Informatics and Applications 44.2 (2010): 229-255. <http://eudml.org/doc/250764>.

@article{Bordihn2010,
abstract = { We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns, pattern expressions, H-systems and uniform substitutions are also investigated. Furthermore, we present their closure properties with respect to TRIO operations and discuss the decidability status and complexity of fixed and general membership, emptiness, and the equivalence problem. },
author = {Bordihn, Henning, Dassow, Jürgen, Holzer, Markus},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Regular languages; homomorphic replacement; computational complexity; regular languages; computational complexity},
language = {eng},
month = {5},
number = {2},
pages = {229-255},
publisher = {EDP Sciences},
title = {Extending regular expressions with homomorphic replacement},
url = {http://eudml.org/doc/250764},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Bordihn, Henning
AU - Dassow, Jürgen
AU - Holzer, Markus
TI - Extending regular expressions with homomorphic replacement
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/5//
PB - EDP Sciences
VL - 44
IS - 2
SP - 229
EP - 255
AB - We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns, pattern expressions, H-systems and uniform substitutions are also investigated. Furthermore, we present their closure properties with respect to TRIO operations and discuss the decidability status and complexity of fixed and general membership, emptiness, and the equivalence problem.
LA - eng
KW - Regular languages; homomorphic replacement; computational complexity; regular languages; computational complexity
UR - http://eudml.org/doc/250764
ER -

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