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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Advanced methods of searching the game tree of 3-dimensional Tic-Tac-Toe
 Dvořák, Pavel ; Valla, Tomáš (advisor) ; Šámal, Robert (referee)
In this thesis we study positional games, especially multidimensional tic-tac-toe. We compare present advanced algorithms (Pn-search, Db-search and λ-search) for position solving in positional games. We apply the algorithms on the do- main of 43 and 53 games, which are the first nontrivial cases of 3-dimensional tic-tac-toe. We parallelize Pn-search for cases when there are more starting po- sitions. We apply Pn-search as a single-thread task and we solve how to share the transposition table with solved positions. Our main and clearly theoretical result is the characterization of the group of all automorphisms of combinatorial cube nd with the same set of lines as multidimensional tic-tac-toe has. This is a generalization of Silver [The American Mathematical Monthly, Vol. 74, No. 3, 1967], who characterized the automorphisms of the game 43 . 1
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Advanced methods of searching the game tree of 3-dimensional Tic-Tac-Toe
 Dvořák, Pavel ; Valla, Tomáš (advisor) ; Šámal, Robert (referee)
In this thesis we study positional games, especially multidimensional tic-tac-toe. We compare present advanced algorithms (Pn-search, Db-search and λ-search) for position solving in positional games. We apply the algorithms on the do- main of 43 and 53 games, which are the first nontrivial cases of 3-dimensional tic-tac-toe. We parallelize Pn-search for cases when there are more starting po- sitions. We apply Pn-search as a single-thread task and we solve how to share the transposition table with solved positions. Our main and clearly theoretical result is the characterization of the group of all automorphisms of combinatorial cube nd with the same set of lines as multidimensional tic-tac-toe has. This is a generalization of Silver [The American Mathematical Monthly, Vol. 74, No. 3, 1967], who characterized the automorphisms of the game 43 . 1
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