Tighter Bounds for the Determinisation of Büchi Automata [chapter]

Sven Schewe
2009 Lecture Notes in Computer Science  
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 ω-word automata are the basis for several manipulations of ω-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
more » ... at 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.
doi:10.1007/978-3-642-00596-1_13 fatcat:lso7d57zzzcz7oe4zyt37qotom