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Subject: Re: is Chess a Hard NP?

Author: José Carlos

Date: 04:37:46 01/21/05

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On January 21, 2005 at 03:50:37, Russell Reagan wrote:

>On January 20, 2005 at 23:18:01, Dann Corbit wrote:
>
>>On the other hand, is Tic-Tac-Toe exponential?
>>Strictly speaking -- yes it is.
>>But even the lamest computer can solve it minimax in a fraction of a second.
>>
>>So there can come to be some point where it no longer matters that it is
>>exponential because the compute speed has caught up to the size of the problem
>>and it has really become O(1).
>>
>>So it is not something that we can just dismiss as irrelevant.  I think this is
>>especially the case when the input is fixed (as in the case of an adversarial
>>game) rather than sorting or something where we might want to sort the cards in
>>a deck, but we might also want to sort all the CTAG sequences in Chrysanthemum
>>DNA.
>
>
>Isn't O-notation used for analyzing situations where N can grow to infinity?
>Describing 3x3 tic-tac-toe in terms of O-notation doesn't really make sense to
>me. For 3x3 tic-tac-toe, what is N? At least for chess, N is practically
>infinity, for now.

  Isn't N meant as the input elements number, like in a sorting algorithm or int
he Salesman problem? Something we may vary and see how that variation affects
the solution time? Chess and tic-tac-toe are constant problems in that sense, so
O-notation doesn't apply, IMHO. You could use, for example, variable size board
for tic-tac-toe, being 3 the minimum, and then ask yourself "how does solution
time increase when I use 4x4 board instead of 3x3? Then you give a sense to
O(N).

  José C.



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