Proof-Set Search

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.