Tighter Bounds for the Determinisation of Büchi Automata

• Authors: Sven Schewe
• Venue: FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
• Year: 2009

The introduction of an efficient determinisation technique for Büchi automata by Safra has been a milestone in automata theory. To name only a few applications, efficient determinisation techniques for *** -word automata are the basis for several manipulations of *** -tree automata (most prominently the nondeterminisation of alternating tree automata) as well as for satisfiability checking and model synthesis for branching- and alternating-time logics. This paper proposes a determinisation technique that is simpler than the constructions of Safra, Piterman, and Muller and Schupp, because it separates the principle acceptance mechanism from the concrete acceptance condition. The principle mechanism intuitively uses a Rabin condition on the transitions; we show how to obtain an equivalent Rabin transition automaton with approximately (1.65 n ) n states from a nondeterministic Büchi automaton with n states. Having established this mechanism, it is simple to develop translations to automata with standard acceptance conditions. We can construct standard Rabin automata whose state-space is bilinear in the size of the input alphabet and the state-space of the Rabin transition automaton, or, for large input alphabets, contains approximately (2.66 n ) n states, respectively. We also provide a flexible translation to parity automata with O (n !2) states and 2n priorities based on a later introduction record, and hence connect the transformation of the acceptance condition to other record based transformations known from the literature.