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a [[Best-First|best-first]] [https://en.wikipedia.org/wiki/And%E2%80%93or_tree and-or tree] search algorithm designed by [[Victor Allis]] for finding the game-theoretical value in game trees <ref>[[Victor Allis]] ('''1994'''). ''Searching for Solutions in Games and Artificial Intelligence''. Ph.D. thesis, [[Maastricht University|University of Limburg]], [http://fragrieu.free.fr/SearchingForSolutions.pdf pdf]</ref> . PNS is based on ideas derived from [[Conspiracy Number Search|conspiracy number search]]. While in cn search the purpose is to continue searching until it is unlikely that the [[Minimax|minimax]] value of the [[Root|root]] will change, PNS aims at '''proving''' the true value of the root <ref>[[Victor Allis]], [[Maarten van der Meulen]], [[Jaap van den Herik]] ('''1994'''). ''[http://www.sciencedirect.com/science/article/pii/0004370294900043 Proof-Number Search]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 66, No. 1</ref> .In the fall 2012 issue of the [[ICGA Journal#35_3|ICGA Journal]], about 20 years after its invention, [[Akihiro Kishimoto]], [[Mark Winands]], [[Martin Müller]] and [[Jahn-Takeshi Saito]] wrote a résumé about PNS and its variants and enhancements, considered a tribute to Victor Allis by editor [[Jaap van den Herik]] <ref>[[Akihiro Kishimoto]], [[Mark Winands]], [[Martin Müller]], [[Jahn-Takeshi Saito]] ('''2012'''). ''Game-Tree Search using Proof Numbers: The First Twenty Years''. [[ICGA Journal#35_3|ICGA Journal, Vol. 35, No. 3]]</ref> <ref>[[Jaap van den Herik]] ('''2012'''). ''All is Proof Numbers''. [[ICGA Journal#35_3|ICGA Journal, Vol. 35, No. 3]] (editorial)</ref> .