Complementing semi-deterministic Büchi automata

Abstract

We introduce an efficient complementation technique for semi-deterministic Büchi automata, which are Büchi automata that are deterministic in the limit: from every accepting state onward, their behaviour is deterministic. It is interesting to study semi-deterministic automata, because they play a role in practical applications of automata theory, such as the analysis of Markov decision processes. Our motivation to study their complementation comes from the termination analysis implemented in ULTIMATE BÜCHI AUTOMIZER, where these automata represent checked runs and have to be complemented to identify runs to be checked. We show that semi-determinism leads to a simpler complementation procedure: an extended breakpoint construction that allows for symbolic implementation. It also leads to significantly improved bounds as the complement of a semi-deterministic automaton with n states has less than 4n states. Moreover, the resulting automaton is unambiguous, which again offers new applications, like the analysis of Markov chains. We have evaluated our construction against the semideterministic automata produced by the Ultimate BÜCHI AUTOMIZER. The evaluation confirms that our algorithm outperforms the known complementation techniques for general nondeterministic Büchi automata.