Abstract
Victor Allis’ proof-number search is a powerful best-first tree search method which can solve games by repeatedly expanding a most-proving node in the game tree. A well-known problem of proof-number search is that it does not account for the effect of transpositions. If the search builds a directed acyclic graph instead of a tree, the same node can be counted more than once, leading to incorrect proof and disproof numbers. While there are exact methods for computing proof numbers in DAGs, they are too slow to be practical.
Proof-set search (PSS) is a new search method which uses a similar value propagation scheme as proof-number search, but backs up proof and disproof sets instead of numbers. While the sets computed by proof-set search are not guaranteed to be of minimal size, they do provide provably tighter bounds than is possible with proof numbers.
The generalization proof-set search with (P,D)-truncated node sets or PSS P,D provides a well-controlled tradeoff between memory requirements and solution quality. Both proof-number search and proof-set search are shown to be special cases of PSS P,D . Both PSS and PSS P,D can utilize heuristic initialization of leaf node costs, as has been proposed in the case of proof-number search by Allis.
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References
Allis, V.: Searching for Solutions in Games and Artificial Intelligence. PhD thesis, University of Limburg, Maastricht (1994)
Schijf, M.: Proof-number search and transpositions. Master’s thesis, University of Leiden (1993)
Schijf, M., Allis, V., Uiterwijk, J.: Proof-number search and transpositions. International Computer Chess Association Journal 17, 63–74 (1994)
Breuker, D., van den Herik, J., Uiterwijk, J., Allis, V.: A solution to the GHI problem for best-first search. In: van den Herik, H.J., Iida, H. (eds.) CG 1998. LNCS, vol. 1558, pp. 25–49. Springer, Heidelberg (1999)
McHugh, J.: Algorithmic Graph Theory. Prentice-Hall, Englewood Cliffs (1990)
Stanley, R.: Enumerative Combinatorics. Cambridge Studies in Advanced Mathematics, vol. 1(49). Cambridge University Press, Cambridge (1997)
Kishimoto, A.: Seminar presentation. Electrotechnical Laboratory, Tsukuba, Japan (1999)
Nagai, A.: DF-PN Algorithm for Searching AND/OR Trees and Its Applications. PhD thesis, University of Tokyo (2001)
Breuker, D., Uiterwijk, J., van den Herik, J.: The PN2-search algorithm. In: van den Herik, J., Monien, B. (eds.) Advances in Computer Games 9, Universiteit Maastricht, pp. 115–132 (2001)
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Müller, M. (2003). Proof-Set Search. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds) Computers and Games. CG 2002. Lecture Notes in Computer Science, vol 2883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40031-8_7
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DOI: https://doi.org/10.1007/978-3-540-40031-8_7
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