The cost of being co-Buchi is nonlinear

Abstract

It is well known, and easy to see, that not each nondeterministic Buchi automaton on infinite words can be simulated by a nondeterministic co-Buchi 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 Buchi automaton with n states, which can be simulated by a nondeterministic co-Buchi automaton, but cannot be simulated by any nondeterministic co-Buchi automaton with less than c*n^{7/6} states for some constant c. This improves on the best previously known lower bound of 3(n-1)/2.