Local Strategy Improvement for Parity Game Solving

TL;DR

This paper introduces a local strategy improvement algorithm for solving parity games that explores the game graph dynamically, outperforming existing global and local algorithms significantly in empirical tests.

Contribution

The paper presents a novel local strategy improvement algorithm that operates on-the-fly, reducing the need for the entire game graph and improving efficiency over prior methods.

Findings

Local strategy improvement outperforms global algorithms by several orders of magnitude.

The new approach is more efficient in scenarios where only parts of the game are relevant.

Empirical results demonstrate significant performance gains over existing algorithms.

Abstract

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present a local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps. We also compare it empirically with existing global strategy improvement algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy improvement can outperform these others by several orders of magnitude.