On the Power of Unambiguity in Büchi Complementation

Abstract

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