State of B\"uchi Complementation

TL;DR

This paper reviews four main approaches to B"uchi automata complementation, proposes optimizations, and experimentally compares their practical performance, highlighting the superiority of the Safra-Piterman method.

Contribution

It provides the first comprehensive experimental comparison of all four major B"uchi automata complementation approaches with optimized heuristics.

Findings

Safra-Piterman outperforms others in smaller complements and efficiency

Heuristics significantly improve Safra-Piterman and slice-based methods

Experimental results guide practical choice of complementation techniques

Abstract

Complementation of B\"uchi automata has been studied for over five decades since the formalism was introduced in 1960. Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and slice-based approaches. Regarding the performance of these approaches, there have been several complexity analyses but very few experimental results. What especially lacks is a comparative experiment on all of the four approaches to see how they perform in practice. In this paper, we review the four approaches, propose several optimization heuristics, and perform comparative experimentation on four representative constructions that are considered the most efficient in each approach. The experimental results show that (1) the determinization-based Safra-Piterman construction outperforms the other three in producing smaller complements and finishing more tasks in the allocated time and (2) the proposed heuristics substantially improve the Safra-Piterman and the slice-based constructions.