The cost of being co-Buchi is nonlinear

TL;DR

This paper demonstrates that the state complexity of simulating nondeterministic Buchi automata with nondeterministic co-Buchi automata can grow nonlinearly, providing new lower bounds on the number of states required.

Contribution

It introduces a sequence of languages showing that the state cost for simulation can grow faster than previously known, establishing a new lower bound of c*n^{7/6}.

Findings

State complexity of co-Buchi simulation can grow nonlinearly.

Established a new lower bound of c*n^{7/6} for state growth.

Improves upon previous lower bounds of 3(n-1)/2.

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.