The complementation problem for Bu¨chi automata with applications to temporal logic
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Parity automata are a generalisation of Büchi automata that have some interesting advantages over the latter, e.g. determinisability, succinctness and the ability to express certain acceptance conditions like the intersection of a Büchi and a co-Büchi condition directly as a parity condition. Decision problems like universality and inclusion for such automata are PSPACE-complete and have originally been tackled via explicit complementation only. Ramsey-based methods are a later development that avoids explicit complementation but relies on an application of Ramsey's Theorem for its correctness. In this paper we develop new and explicit Ramsey-based algorithms for the universality and inclusion problem for nondeterministic parity automata. We compare them to Ramsey-based algorithms which are obtained from translating parity automata into Büchi automata first and then applying the known Ramsey-based analysis procedures to the resulting automata. We show that the speed-up in the asymptotic worst-case gained through the new and direct methods is exponential in the number of priorities in the parity automata. We also show that the new algorithms are much more efficient in practice.