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.
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