On the Power of Unambiguity in Büchi Complementation
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In this work, we exploit the power of unambiguity for the complementation problem of Büchi automata by utilizing reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor. Given a Büchi automaton with n states and a finite degree of ambiguity, we show that the number of states in the complementary Büchi automaton constructed by the classical Rank-based and Slice-based complementation constructions can be improved, respectively, to 2^O(n) from 2^O( n log n) and to O(4^n) from O( (3n)^n), based on reduced run DAGs. To the best of our knowledge, the improved complexity is exponentially better than best known result of O(5^n) in [21] for complementing Büchi automata with a finite degree of ambiguity.
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