# Determinization of B\"uchi Automata: Unifying the Approaches of Safra and Muller-Schupp

## TL;DR

This paper introduces a unified determinization method for B"uchi automata that combines Safra's and Muller-Schupp's approaches, enabling improved heuristics and a deeper understanding of the structures involved.

## Contribution

A new meta-construction that subsumes both Safra's and Muller-Schupp's determinization procedures for B"uchi automata, based on a novel correspondence between their structural representations.

## Key findings

- The new construction strictly subsumes both existing methods.
- It reveals a correspondence between Safra trees and Muller-Schupp levels.
- The approach enables combining existing techniques and developing heuristics.

## Abstract

Determinization of B\"uchi automata is a long-known difficult problem and after the seminal result of Safra, who developed the first asymptotically optimal construction from B\"uchi into Rabin automata, much work went into improving, simplifying or avoiding Safra's construction. A different, less known determinization construction was derived by Muller and Schupp and appears to be unrelated to Safra's construction on the first sight. In this paper we propose a new meta-construction from nondeterministic B\"uchi to deterministic parity automata which strictly subsumes both the construction of Safra and the construction of Muller and Schupp. It is based on a correspondence between structures that are encoded in the macrostates of the determinization procedures - Safra trees on one hand, and levels of the split-tree, which underlies the Muller and Schupp construction, on the other. Our construction allows for combining the mentioned constructions and opens up new directions for the development of heuristics.