Proof-Set Search [chapter]

Martin Müller
2003 Lecture Notes in Computer Science  
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 DAG's, they
more » ... 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 È ËË È 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 È ËË È . Both PSS and È ËË È can utilize heuristic initialization of leaf node costs, as has been proposed in the case of proof-number search by Allis. 1. Ö is the root of ×. 2. In all leaf nodes of ×, the predicate È is well-defined and evaluates to true. 3. If Ò is an AND node in ×, then all of its successor nodes in the game tree are also contained in ×. Analogous properties hold for a disproof tree × of Ö: 1. Ö is the root of ×.
doi:10.1007/978-3-540-40031-8_7 fatcat:styax22dgzhf3ks32pjbk5me7q