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Subject: Re: Chess and O(1)

Author: Ricardo Gibert

Date: 11:05:16 05/09/01

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On May 09, 2001 at 14:03:01, Dann Corbit wrote:

>On May 09, 2001 at 13:50:33, Ricardo Gibert wrote:
>
>>On May 09, 2001 at 13:47:32, Jeremiah Penery wrote:
>>
>>>A lot of people seem to be saying that chess can be solved by an O(1),
>>>constant-time, algorithm.  Technically, this may be true.  _IF_ you had the
>>>proper algorithm that was capable of computing chess exactly[1], it could
>>>exhibit constant-time behavior.  The problems are that no such algorithm exists
>>>today, and the constant would be so large as to have no relevant meaning in
>>>today's world - i.e., it would likely be greater than the age of the universe.
>>>All chess programs are currently using some sort of tree-searching algorithm
>>>(Alpha-Beta or variant), which are provably O(exp(n)) algorithms.  Time
>>>increases exponentially with the increase in input depth - depth 5 takes
>>>exponentially less time than depth 6, which in turn takes exponentially less
>>>time than depth 7, and so on.  The fact that depth _eventually_ ends _IN CHESS_,
>>>has nothing to do with the complexity of the algorithm.  Theoretically you can
>>>give the same algorithm an infinitely sized tree, so that constant-time solution
>>>is impossible.  For those who say that chess is O(1), it can't be so if the
>>>program in question is using a tree-search algorithm!
>>>
>>>
>>>[1] This O(1) chess algorithm would have to solve the game not by computing a
>>>tree, because tree-search is demonstrably O(exp(n)) for this type of tree.
>>
>>That it is a tree is not relevant. The tree is finite. That's enough.
>
>So your requirement is that the tree is infinite?
>
>As popeye the sailor says:
>"Uck, uck uck, uck."

A finite constant to be precise.

I've been polite and expect you to do the same.



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