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 e...