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We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to Büchi, Streett, and Emerson and Lei (EL), and we study their computational properties. Our finding is that Büchi, Streett, and EL automata span a spectrum of succinctness. EL automata are exponentially more succinct than Büchi automata, and complementation of EL automata is doubly exponential. Streett automata are of intermediate complexity. While translating from Streett automata to Büchi automata involves an exponential blow-up, so does the translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more succinct than Büchi automata, complementation of Streett automata is only exponential. As a result, we show that the decision problem for ETLEL, where temporal connectives are represented by EL automata, is EXPSPACE-complete, and the decision problem for ETLS, where temporal connectives are represented by Streett automata, is PSPACE-complete.