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Extending regular expressions with homomorphic replacement

Published online by Cambridge University Press:  26 January 2010

Henning Bordihn ,
Jürgen Dassow  and
Markus Holzer
Henning Bordihn
Affiliation:
Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482 Potsdam, Germany.
Jürgen Dassow
Affiliation:
Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany.
Markus Holzer
Affiliation:
Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392 Giessen, Germany; holzer@informatik.uni-giessen.de
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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.

Keywords

Regular languageshomomorphic replacementcomputational complexity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 2 , April 2010 , pp. 229 - 255
Copyright
© EDP Sciences, 2010

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