Implementation of Proof-Number search variants in Python

Proof-Number search (PNS) is a best-first tree search algorithm applied to determine the definite value of AND/OR trees. PNS does not require domain knowledge, only terminal positions need to be recognized. PNS can be used to solve games and endgame positions.

PN* is a variant of PNS, which transforms the best-first approach to a depth-first search. PN* applies iterative deepening as a means to solve for memory problems that can arise in PNS, which keeps the entire tree in memory. Not only does PN* apply multiple iterative deepening at the root node but also at all interior OR nodes.

Proof-number and Disproof-number search (PDS) is an extension to the PN* algorithm. PDS is a depth-first multiple iterative-deepening algorithm and uses pn and dpn to set thresholds for the search process. By using thresholds for dpn, PDS extends PN* in not only performing multiple iterative deepening at OR nodes but also at AND nodes. pn and dpn thresholds are given to a node and the subtree is searched while pn and dpn are within the thresholds.

Another depth-first variant of PNS is depth-first proof-number search (df-pn). Unlike in PN* and PDS, no iterative deepening is performed at the root node. df-pn uses thresholds for pn and dpn. pn thresholds are called pnt and dpn thresholds dnt. df-pn initializes pnt and dnt with infinity and searches subtrees within the thresholds. The search terminates when a solution to the tree has been found.