Proof-number search

Allis, L.V.; Meulen, Maarten van der; Herik, H.J. van den

doi:10.1016/0004-3702(94)90004-3

Cited by 134 publications

(113 citation statements)

References 17 publications

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“…Proof-Number Search (PNS) by Allis et al (1994) is the original search algorithm using proof numbers. All other variants of proof-number search are descendants of PNS.…”

Section: Proof-number Searchmentioning

confidence: 99%

“…His solver uses the PNS variant PN* (Seo, 1995;Seo et al, 2001). Allis et al (1994) introduce two pruning techniques that remove useless nodes from the search tree. (1) DeleteSolvedSubtree deletes all subtrees with proof or disproof number equal to 0 when an ancestor is proven or disproven by backpropagation.…”

Section: Transposition Table and Replacement Strategiesmentioning

confidence: 99%

“…Let bf(n) be the branching factor at leaf node n. A popular initialization rule (Allis, 1988;Allis et al, 1994;Breuker, Allis, and van den Herik, 1994;Winands, 2004) sets dn(n) = bf(n), pn(n) = 1 for OR nodes and pn(n) = bf(n), dn(n) = 1 for AND nodes. Effectively, this initialization rule adds an additional ply of search tree information without changing the characteristics of PNS variants, and it results in improved performance.…”

Section: Initialization Of Proof and Disproof Numbersmentioning

confidence: 99%

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Game-Tree Search Using Proof Numbers: The First Twenty Years

Kishimoto¹,

Winands²,

Müller³

et al. 2012

ICG

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Solving games is a challenging and attractive task in the domain of Artificial Intelligence. Despite enormous progress, solving increasingly difficult games or game positions continues to pose hard technical challenges. Over the last twenty years, algorithms based on the concept of proof and disproof numbers have become dominating techniques for game solving. Prominent examples include solving the game of checkers to be a draw, and developing checkmate solvers for shogi, which can find mates that take over a thousand moves. This article provides an overview of the research on Proof-Number Search and its many variants and enhancements.

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“…Proof-Number Search (PNS) by Allis et al (1994) is the original search algorithm using proof numbers. All other variants of proof-number search are descendants of PNS.…”

Section: Proof-number Searchmentioning

confidence: 99%

Section: Transposition Table and Replacement Strategiesmentioning

confidence: 99%

Section: Initialization Of Proof and Disproof Numbersmentioning

confidence: 99%

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Game-Tree Search Using Proof Numbers: The First Twenty Years

Kishimoto¹,

Winands²,

Müller³

et al. 2012

ICG

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“…Instead, we must modify their search process as described in Allis, van der Meulen, and van den Herik (1994): given a result to prove (e.g. white wins by 5 points), we tag leaf nodes as true if their value is equal or superior to this result, and false otherwise.…”

Section: Solving Subgamesmentioning

confidence: 99%

“…For this task, it is possible either to use a traditional solver (adapted with the procedure presented in Section 2.2) like Proof-Number Search (PNS) (Allis et al, 1994) or some of its variants, or to use a more traditional Amazons engine, be it a traditional Alpha/Beta engine (Lieberum, 2005) or a more recent MCTS engine (Kloetzer et al, 2007;Lorentz, 2008).…”

Section: Playing Amazons Endgamesmentioning

confidence: 99%

Playing Amazons Endgames1

Kloetzer¹,

Iida²,

Bouzy³

2009

ICG

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The game of the Amazons is a fairly young member of the class of territory-games. Since there is very few human play, it is difficult to estimate the level of current programs. However, it is believed that humans could play much stronger than todays programs, given enough training and incentives. With the more general goal of improving the playing level of Amazons programs in mind, we focused here on the playing of endgames situations. Our comparative study of two solvers, DFPN and WPNS, and three game-playing algorithms, Minimax with Alpha/Beta, Monte-Carlo Tree-Search and Temperature Discovery Search, shows that even though their computing process is quite expensive, traditional PNS-based solvers are best suited for the task of finding moves in a subgame, while no specific improvement is needed to classical game-playing engines to play well combinations of subgames. Even the new Amazons standard of Monte-Carlo Tree-Search, despite showing often weaknesses in precise tasks like solving, handles Amazons endgames pretty well.

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Selective Approaches for Solving Weak Games

Helmert

Mattmüller

Schewe

2006

Automated Technology for Verification and Analysis

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Abstract. Model-checking alternating-time properties has recently attracted much interest in the verification of distributed protocols. While checking the validity of a specification in alternating-time temporal logic (ATL) against an explicit model is cheap (linear in the size of the formula and the model), the problem becomes EXPTIME-hard when symbolic models are considered. Practical ATL model-checking therefore often consumes too much computation time to be tractable. In this paper, we describe a novel approach for ATL model-checking, which constructs an explicit weak model-checking game on-the-fly. This game is then evaluated using heuristic techniques inspired by efficient evaluation algorithms for and/or-trees. To show the feasibility of our approach, we compare its performance to the ATL model-checking system MOCHA on some practical examples. Using very limited heuristic guidance, we achieve a significant speedup on these benchmarks.

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Proof-number search

Cited by 134 publications

References 17 publications

Game-Tree Search Using Proof Numbers: The First Twenty Years

Game-Tree Search Using Proof Numbers: The First Twenty Years

Playing Amazons Endgames1

Selective Approaches for Solving Weak Games

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