Succinctness of Regular Expressions with Interleaving, Intersection and Counting

Abstract

Studying the impact of operations, such as intersection and interleaving, on the succinctness of regular expressions has recently received renewed attention [12,13,14]. 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 can not 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 can not 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.