About the Completeness of Depth-First Proof-Number Search

Abstract. Depth-first proof-number (df-pn) search is a powerful member of the family of algorithms based on proof and disproof numbers. While df-pn has succeeded in practice, its theoretical properties remain poorly understood. This paper resolves the question of completeness of df-pn: its ability to solve any finite boolean-valued game tree search problem in principle, given unlimited amounts of time and memory. The main results are that df-pn is complete on finite directed acyclic graphs (DAG) but incomplete on finite directed cyclic graphs (DCG).

• Type: Conference
• Year: 2008
• Where: CG
• Authors: Akihiro Kishimoto, Martin Müller 0003
• Keywords: CG 2008, Computer Graphics, Depth-first Proof-number, Finite Boolean-valued Game, Tree Search Problem