On ! - Automata and Temporal Logi

We study here the use of di erent representation for in nitary regular languages in extended temporal logi . We fo us on three di erent kinds of a eptan e onditions for nite automata on in nite words, due to B u hi, Streett, and Emerson and Lei (EL), and we study their omputational properties. Our nding is that B u hi, Streett, and EL automata span a spe trum of su in tness. EL automata are exponentially more su in t than B u hi automata, and omplementation of EL automata is doubly exponential. Streett automata are of intermediate omplexity. While translating from Streett automata to B u hi automata involves an exponential blow-up, so does the translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more su in t than B u hi automata, omplementation of Streett automata is only exponential. As a result, we show that the de ision problem for ETL EL , where temporal onne tives are represented by EL automata, is EXPSPACEomplete, and the de ision problem for ETL S , where temporal onne tives are represented by Streett automata, is PSPACEomplete.