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### Subject: Re: Zappa Report

Author: Ingo Althofer

Date: 04:01:46 12/31/05

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On December 31, 2005 at 04:38:46, Rafael Andrist wrote:
>On December 30, 2005 at 13:02:43, Ingo Althofer wrote:
>>... in case of linear evaluation functions with lots
>>of terms there is always a small subset of the terms
>>such that this set with the right parameters is
>>almost as good as the full evaluation function.
>
> Can you state this a bit more precise, please?
> As long as it is not clear what you mean by "lots of" and "small"
> and "almost as good", your statement says nothing and could be
> trivially true, if, for ex.
> "small" just means "less or equal".
I can assure you that the result is not trivial.
Unfortunately I wrote the paper, before the
mathematical community developed fully "electronized"
publication services. So you have to look at the
paper versions:
The technical result with complete proofs is given in
* I. Althofer. On sparse approximations to randomized strategies and convex
combinations. Linear Algebra and Applications 199 (1994), 339-355.
The application to linear evaluation functions in chess, go,
and other games is described in
* I. Althofer. On telescoping linear evaluation functions.
ICCA-J , Vol 16 (1993), pp. 91-94 (issue June 1993).
Funnily, in this context "Go" seems to be only about
2-3 times more complicated than chess, if I remember correctly.
(... where complexity is measured in number of linear terms needed to
achieve a certain level of quality)
Regards, Ingo Althofer.

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