Succinctness of regular expressions with interleaving, intersection and counting

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Abstract

In this paper, we study the succinctness of regular expressions (REs) extended with interleaving, intersection and counting operators. We show that in a translation from REs with interleaving to standard regular expressions a double exponential size increase cannot be avoided. We also consider the complexity of translations to finite automata. We give a tight exponential lower bound on the translation of REs with intersection to NFAs, and, for each of the three classes of REs, we show that in a translation to a DFA a double exponential size increase cannot be avoided. Together with known results, this gives a complete picture of the complexity of translating REs extended with interleaving, intersection or counting into (standard) regular expressions, NFAs, and DFAs.

Keywords

Regular Expressions
Succinctness

Cited by (0)

An extended abstract of this paper appeared in the proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2008).

1

Research Assistant of the Fund for Scientific Research - Flanders (Belgium).