Proving correctness of a KRK chess endgame strategy by sat-based constraint solving

Abstract

Chess endgame strategies describe, in a concise and intuitive way, the rules that a player should follow to ensure a win (or a draw). Endgame strategies are useful for both computer and human players. Their correctness can be proved in several ways. In this article we present one of them: a computer assisted proof based on reduction to propositional logic, more precisely to SAT. We focus on a strategy for the KRK endgame. The reduction to SAT is performed by using a constraint solving system URSA. The relevant lemmas produced SAT instances with hundreds or even thousands of variables and clauses, but URSA still successfully handled them. We would like to emphasise that this is the first computer-assisted high-level proof of the correctness of a strategy for some chess endgame. The presented methodology can be applied to other endgames and other games as well. Therefore, the point of this article is not only presenting a proof of correctness of an endgame strategy, but also presenting a new methodology for computer-assisted reasoning about chess endgames.