Reducing (To) the Ranks: Efficient Rank-Based Büchi Automata Complementation

Authors Vojtěch Havlena , Ondřej Lengál

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Vojtěch Havlena
  • Faculty of Information Technology, Brno University of Technology, Czech Republic
Ondřej Lengál
  • Faculty of Information Technology, Brno University of Technology, Czech Republic


We thank reviewers of this and previously submitted versions of the paper for their useful remarks that helped us improve the quality of the paper. This work was supported by the Czech Science Foundation project 20-07487S and the FIT BUT internal project FIT-S-20-6427.

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Vojtěch Havlena and Ondřej Lengál. Reducing (To) the Ranks: Efficient Rank-Based Büchi Automata Complementation. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


This paper provides several optimizations of the rank-based approach for complementing Büchi automata. We start with Schewe’s theoretically optimal construction and develop a set of techniques for pruning its state space that are key to obtaining small complement automata in practice. In particular, the reductions (except one) have the property that they preserve (at least some) so-called super-tight runs, which are runs whose ranking is as tight as possible. Our evaluation on a large benchmark shows that the optimizations indeed significantly help the rank-based approach and that, in a large number of cases, the obtained complement is the smallest from those produced by state-of-the-art tools for Büchi complementation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Büchi automata
  • rank-based complementation
  • super-tight runs


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