Memoryless Determinacy of Infinite Parity Games: Another Simple Proof

TL;DR

This paper presents two simplified, trap- and attractor-free proofs of memoryless determinacy for infinite parity games, adapting techniques from finite cases to extend understanding of these complex games.

Contribution

It introduces novel, simplified proofs for infinite parity games' memoryless determinacy, avoiding traditional trap and attractor methods.

Findings

Two new proofs of infinite parity games' determinacy

Shorter and more constructive proof approaches

Elimination of traps and attractors in proofs

Abstract

In 1998 Zielonka simplified the proofs of memoryless determinacy of infinite parity games. In 2018 Haddad simplified some proofs of memoryless determinacy of finite parity games. This article adapts Haddad's technique for infinite parity games. Two proofs are given, a shorter one and a more constructive one. None of them uses Zielonka's traps and attractors.