Lambda Depth-first Proof Number Search and its Application to Go

Kazuki Yoshizoe, Akihiro Kishimoto, Martin Müller

Thomsen's λ search and Nagai's depth-first proof-number (DFPN) search are two powerful but very different AND/OR tree search algorithms. Lambda Depth-First Proof Number search (LDFPN) is a novel algorithm that combines ideas from both algorithms. λ search can dramatically reduce a search space by finding different levels of threat sequences. DFPN employs the notion of proof and disproof numbers to expand nodes expected to be easiest to prove or disprove. The method was shown to be effective for many games. Integrating λ order with proof and disproof numbers enables LDFPN to select moves more effectively, while preserving the efficiency of DFPN. LDFPN has been implemented for capturing problems in Go and is shown to be more efficient than DFPN and more robust than an algorithm based on classical λ search.