Abstract:
We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (!-automata). An!-automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. It may be either deterministic or nondeterministic, and may have different types of acceptance condition. Our main result is a new, simpler, determinization construction that yields a single exponent upper bound for the translation of any Buchi nondeterministic!-automaton into a deterministic!-auomaton. This construction is optimal. We also look at the complexity of the complementation problem for different types of!-automata, and, among other results, obtain an exponential complementation for Streett!-automata. These results can be used to improve the complexity of decision procedures for different logics that use automata-theoretic techniques.
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