# Can Nondeterminism Help Complementation?

Special Issue of Theoretical Computer Science for GandALF 2012.

### Abstract

Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Theta(2textasciicircumn) where n is the state size. The same similarity between determinization and complementation was found for Buchi automata, where both operations were shown to have 2textasciicircumTheta(n lg n) state complexity. An intriguing question is whether there exists a type of omega-automata whose determinization is considerably harder than its complementation. In this paper, we show that for all common types of omega-automata, the determinization problem has the same state complexity as the corresponding complementation problem at the granularity of 2textasciicircumTheta(.).

Publication

*Electronic Proceedings in Theoretical Computer Science*