Tight Bounds for Complementing Parity Automata

TL;DR

This paper presents a tight complementation procedure for parity automata, establishing bounds that are close to optimal and independent of the number of priorities, advancing the understanding of automata determinisation.

Contribution

It introduces a new complementation method from parity automata to nondeterministic Büchi automata with tight bounds up to an O(n) factor, independent of priorities.

Findings

Complementation procedure is tight up to an O(n) factor.

Bound does not depend on the number of priorities.

Advances the theoretical understanding of automata complementation.

Abstract

We follow a connection between tight determinisation and complementation and establish a complementation procedure from parity automata to nondeterministic B\"uchi automata and prove it to be tight up to an $O(n)$ factor, where $n$ is the size of the nondeterministic parity automaton. This factor does not depend on the number of priorities.