One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata

We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic B"uchi automata, and nondeterministic B"uchi automata. The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive boolean combination of languages that can be translated into ω-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed.