# Succinct progress measures for solving parity games

## TL;DR

This paper introduces a new quasi-polynomial time algorithm for solving parity games using succinct progress measures, significantly reducing space complexity through novel tree coding techniques.

## Contribution

It presents an alternative quasi-polynomial algorithm based on progress measures, utilizing innovative ordered tree coding and bounded adaptive multi-counters.

## Key findings

- Reduced space complexity from quasi-polynomial to nearly linear
- Developed novel ordered tree coding techniques
- Proved a succinct tree coding result using bounded adaptive multi-counters

## Abstract

The recent breakthrough paper by Calude et al. has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential. We devise an alternative quasi-polynomial time algorithm based on progress measures, which allows us to reduce the space required from quasi-polynomial to nearly linear. Our key technical tools are a novel concept of ordered tree coding, and a succinct tree coding result that we prove using bounded adaptive multi-counters, both of which are interesting in their own right.