State of B\"uchi Complementation

Abstract

Complementation of B\"uchi automata has been studied for over five decadessince the formalism was introduced in 1960. Known complementation constructionscan be classified into Ramsey-based, determinization-based, rank-based, andslice-based approaches. Regarding the performance of these approaches, therehave been several complexity analyses but very few experimental results. Whatespecially lacks is a comparative experiment on all of the four approaches tosee how they perform in practice. In this paper, we review the four approaches,propose several optimization heuristics, and perform comparativeexperimentation on four representative constructions that are considered themost efficient in each approach. The experimental results show that (1) thedeterminization-based Safra-Piterman construction outperforms the other threein producing smaller complements and finishing more tasks in the allocated timeand (2) the proposed heuristics substantially improve the Safra-Piterman andthe slice-based constructions.Comment: 28 pages, 4 figures, a preliminary version of this paper appeared in the Proceedings of the 15th International Conference on Implementation and Application of Automata (CIAA