Tight Bounds on the Descriptional Complexity of Regular Expressions

Authors:
Hermann Gruber;Markus Holzer
Affiliations:
Institut für Informatik, Universität Giessen, Giessen, Germany D-35392;Institut für Informatik, Universität Giessen, Giessen, Germany D-35392
Venue:
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Year:
2009

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Abstract

We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite automata to regular expressions, study the effect of the complementation operation on the descriptional complexity of regular expressions, and the conversion of regular expressions extended by adding intersection or interleaving to ordinary regular expressions. Almost all obtained lower bounds are optimal, and the presented examples are over a binary alphabet, which is best possible.