Solving Witness-type Triangle Puzzles Faster with an Automatically Learned Human-Explainable Predicate

TL;DR

This paper introduces an automatically learned human-explainable predicate that significantly accelerates search-based puzzle solving in The Witness, enabling faster solutions and handling larger puzzle instances without losing completeness.

Contribution

We develop a novel learned predicate that prunes search states in puzzle solving, improving efficiency and scalability while maintaining correctness.

Findings

Accelerates puzzle solving by an average of six times.

Enables solving larger puzzle instances within fixed time budgets.

Maintains completeness of the search despite pruning.

Abstract

Automatically solving puzzle instances in the game The Witness can guide players toward solutions and help puzzle designers generate better puzzles. In the latter case such an Artificial Intelligence puzzle solver can inform a human puzzle designer and procedural puzzle generator to produce better instances. The puzzles, however, are combinatorially difficult and search-based solvers can require large amounts of time and memory. We accelerate such search by automatically learning a human-explainable predicate that predicts whether a partial path to a Witness-type puzzle is not completable to a solution path. We prove a key property of the learned predicate which allows us to use it for pruning successor states in search thereby accelerating search by an average of six times while maintaining completeness of the underlying search. Conversely given a fixed search time budget per puzzle our predicate-accelerated search can solve more puzzle instances of larger sizes than the baseline search.