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).
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Kishimoto, A., Müller, M. (2008). About the Completeness of Depth-First Proof-Number Search. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds) Computers and Games. CG 2008. Lecture Notes in Computer Science, vol 5131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87608-3_14
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DOI: https://doi.org/10.1007/978-3-540-87608-3_14
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