Many game-playing programs must search very large game trees. Use of the alpha-beta pruning algorithm instead of the simple minimax search reduces by a large factor the number of bottom positions which must be examined in the search. An analytical expression for the expected number of bottom positions examined in a game tree using alpha-beta pruning is derived, subject to the assumptions that t...

Asymptotic lower bounds on the code rate when the encoder and decoder have some partial knowledge about the positions, where the errors may occur during transmission of a codeword are derived.