Extending regular expressions with homomorphic replacement
Institut für Informatik,
Universität Potsdam, August-Bebel-Straße 89,
14482 Potsdam, Germany.
2 Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany.
3 Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392 Giessen, Germany; email@example.com
Accepted: 19 November 2009
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.
Mathematics Subject Classification: 03D40 / 68Q42 / 68Q45
Key words: Regular languages / homomorphic replacement / computational complexity
© EDP Sciences, 2010