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This paper provides several optimizations of the rank-based approach forcomplementing B\"{u}chi automata. We start with Schewe's theoretically optimalconstruction and develop a set of techniques for pruning its state space thatare key to obtaining small complement automata in practice. In particular, thereductions (except one) have the property that they preserve (at least some)so-called super-tight runs, which are runs whose ranking is as tight aspossible. Our evaluation on a large benchmark shows that the optimizationsindeed significantly help the rank-based approach and that, in a large numberof cases, the obtained complement is the smallest from those produced by alarge number of state-of-the-art tools for B\"{u}chi complementation.

Reducing (to) the Ranks: Efficient Rank-based B\"{u}chi Automata Complementation (Technical Report)