Constraint Propagation for Reasoning in Single-Player Deduction Games

Fandi Meng, Kaijie Xu, Simon M. Lucas

Abstract: Single-player deduction games are a canonical form of hidden-information reasoning. Agents iteratively issue actions (queries) and receive deterministic feedback, thereby shrinking the information set of feasible secret codes. Classical search techniques-such as Information-Set Monte-Carlo Tree Search (ISMCTS) or the entropy-driven Information-Set Entropy Search (ISES)-handle these games by sampling or by fully enumerating states, but both methods encounter difficulties when the combinatorial space explodes. This paper introduces a constraintpropagation variant of ISES that models the information set as a constraint-satisfaction problem (CSP) and applies the AC-3 arcconsistency algorithm after every observation. By aggressively pruning unsupported variable values before entropy evaluation, the method eliminates a large number of impossible states and accelerates inference without sacrificing optimality. Using several single-player deduction games from the Deduction Game Framework as case studies, we show that constraint propagation significantly enhances the efficiency of ISES.