Abstract
In this paper, a theory of game tree algorithms is presented, entirely based upon the concept of solution tree. During execution of a game tree algorithm, one may distinguish between so-called alive and dead nodes. It will turn out, that only alive nodes have to be considered, whereas dead nodes should be neglected. The algorithm may stop, when every node is dead. Further, it is proved that every algorithm needs to build a critical tree. Finally, we show, that some common game tree algorithms agree with this theory.
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References
L. Victor Allis, Maarten van der Meulen, and H. Jaap van den Herik, Proofnumber search, Artificial Intelligence 66 (1994), pp. 91–124.
A. de Bruin, W. Pijls, Trends in Game Tree Search, Proceedings Sofsem '96, Theory and Practice of Informatics (Keith G. Jeffery et al. eds.), LNCS vol. 1175, 1996, pp. 255–274.
Toshihide Ibaraki, Generalization of alpha-beta and SSS* search procedures, Artificial Intelligence 29 (1986), pp. 73–117.
Toshihide Ibaraki, Search Algorithms for Minimax Game Trees, Conference paper Twenty years NP-completeness, Sicily, June 1991.
V. Kumar and L.N. Kanal, A General Branch and Bound Formulation for Understanding and Synthesizing And/Or Tree Search Procedures, Artificial Intelligence 21 (1983), pp. 179–198.
Donald E. Knuth and Ronald W. Moore, An analysis of alpha-beta pruning, Artificial Intelligence 6 (1975), no. 4, pp. 293–326.
Wim Pijls, Arie de Bruin, Aske Plaat, A theory of game trees, based on solution trees, Tech. Report EUR-CS-96-06, Erasmus University Rotterdam, December 1996, also available as: http://www. cs. few. eur.nl/few/inf/publicaties/rapporten.eur-few-cs-96-06. ps
Aske Plaat, Jonathan Schaeffer, Wim Pijls and Arie de Bruin, Best-first fixed depth game tree search in practice, Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95), vol. 1, pp. 273–279.
Aske Plaat, Jonathan Schaeffer, Wim Pijls and Arie de Bruin, A Minimax Algorithm Better than SSS*, Artificial Intelligence 84 (1996) pp. 299–337.
G. Stockman, A minimax algorithm better than alpha-beta?, Artificial Intelligence 12 (1979), no. 2, pp. 179–196.
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© 1997 Springer-Verlag Berlin Heidelberg
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Pijls, W., de Bruin, A. (1997). A theory of game trees, based on solution trees. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_136
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DOI: https://doi.org/10.1007/3-540-63774-5_136
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