A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata

In this paper we establish a lower bound hist(n) for the problem of translating a Büchi word automaton of size n into a deterministic Rabin word automaton when both the Büchi and the Rabin condition label transitions rather than states. This lower bound exactly matches the known upper bound to this problem. The function hist(n) is in Ω((1.64n)) and in o((1.65n)). Our result entails a lower bound of hist(n − 1) when the input Büchi automaton has its Büchi acceptance condition labeling states (as it is usual). Those lower bounds remain when the output deterministic Rabin automaton has its Rabin acceptance condition labeling states.