The cost of being co-Buchi is nonlinear

It is well known, and easy to see, that not each nondeterministic Büchi automaton on in nite words can be simulated by a nondeterministic co-Büchi automaton. We show that in the cases when such a simulation is possible, the number of states needed for it can grow nonlinearly. More precisely, we show a sequence of as we believe, simple and elegant languages which witness the existence of a nondeterministic Büchi automaton with n states, which can be simulated by a nondeterministic co-Büchi automaton, but cannot be simulated by any nondeterministic co-Büchi automaton with less than c ∗ n states for some constant c. This improves on the best previously known lower bound of 3(n− 1)/2.