Proof-Set Search

Abstract

Victor Allis’ proof-number search is a powerful best-first tree search method which can solve games by repeatedly expanding a most-proving node in the game tree. A well-known problem of proof-number search is that it does not account for the effect of transpositions. If the search builds a directed acyclic graph instead of a tree, the same node can be counted more than once, leading to incorrect proof and disproof numbers. While there are exact methods for computing proof numbers in DAGs, they are too slow to be practical.

Proof-set search (PSS) is a new search method which uses a similar value propagation scheme as proof-number search, but backs up proof and disproof sets instead of numbers. While the sets computed by proof-set search are not guaranteed to be of minimal size, they do provide provably tighter bounds than is possible with proof numbers.

The generalization proof-set search with (P,D)-truncated node sets or PSS _P,D provides a well-controlled tradeoff between memory requirements and solution quality. Both proof-number search and proof-set search are shown to be special cases of PSS _P,D . Both PSS and PSS _P,D can utilize heuristic initialization of leaf node costs, as has been proposed in the case of proof-number search by Allis.