Compressed Game Solving

TL;DR

This paper introduces a novel approach to solving board games by using compressed string-based representations for move generation, enabling efficient solving of large state spaces with sublinear space complexity.

Contribution

It presents a new method for move generation using compressed sets, achieving sublinear space and near-linear time performance in solving board games.

Findings

Achieved compressed representations for Breakthrough using roughly n^{0.5} to n^{0.7} space.

Demonstrated near-linear time move generation based on compressed sets.

Enabled strong solving of board games with sublinear space complexity.

Abstract

We recast move generators for solving board games as operations on compressed sets of strings. We aim for compressed representations with space sublinear in the number of game positions for interesting sets of positions, move generation in time roughly linear in the compressed size and membership tests in constant time. To the extent that we achieve these tradeoffs empirically, we can strongly solve board games in time sublinear in the state space. We demonstrate this concept with the game Breakthrough where we empirically realize compressed representations taking roughly $n^{0.5}$ to $n^{0.7}$ space to store relevant sets of $n$ positions.