Author: Jesper Antonsson
Date: 13:54:34 05/17/01
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On May 17, 2001 at 05:37:46, Jeremiah Penery wrote: >I found some very nice notes on O(f(n)). >http://theory.lcs.mit.edu/classes/6.042/spring01/handouts/l11.pdf > >On May 16, 2001 at 16:33:29, Jesper Antonsson wrote: >>On May 15, 2001 at 20:53:49, Jeremiah Penery wrote: >>>On May 15, 2001 at 18:11:57, Jesper Antonsson wrote: >> >>>>Most of us are talking about chess and "n" as "target search depth". >>> >>>With the current tree-searching algorithms, do you not agree that depth N+1 >>>takes exponentially longer than depth N? >> >>I'm not talking about generalized tree search algorithms, I'm talking about >>specific chess algorithms. Chess algorithms do a tree search, but the rules of >>chess (which are also part of the algorithm) limit the size of the tree. > >The rules of chess are _not_ part of the alpha-beta search algorithm. No, but part of the chess algorithms used in chess programs. > They are >artificial constraints placed upon the tree size for the particular state-space >of chess. Yes, but those constraints are a part of the algorithms. >If they _were_ part of the algorithm, then a "good" chess algorithm would >simply not search to depths > x, where x is the needed solution depth. Quite right. >So the input becomes bounded - what now? No, it doesn't. You can still input larger depths. It's just like you can set a chess programs max depth to 12 but use a position which yields mate in 6. It will find the mate, but the input wasn't bounded to 6. > O(1) again? And does this mean that any algorithm >where input is bounded is also O(1)? No. >>Therefore, for ("good") chess algorithms and for large N, N+1 won't take take >>longer than N. >> >>>(Ignore the fact that N has a maximum >>>bound - that is completely irrelevant, and has nothing to do with complexity >>>analysis.) >> >>This is not a fact. N is unbounded. I can input a target search depth of a >>million or whatever to a chess algorithm. It will only *search* to a much >>smaller depth, of course, but *that* is irrelevant. > >I think you know what I meant. N is practically bounded by the depth of the >chess-tree in this case. But you can input larger depths to the algorithm.
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