Re: Testvectors

Mok-Kong Shen (mok-kong.shent-online.de)
Tue, 07 Sep 1999 02:42:28 +0200

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Ben Laurie wrote:
>
> There is not a known way to avoid uncomputability without also removing
> the ability to compute some computables things. Unfortunately, it isn't
> known how to prove this, either, though if you can prove Church's
> Thesis, you are away...

I doubt that I fully understand your first sentence. That
uncomputability exists is, I presume, what you accept. Now everything
minus the uncomputables gives just what is computable, isn't it?
Of course this isn't a practically useful concept. On the other hand
I wonder whether people handling real-life problems (including crypto
applications) really needs to be concerned about the 'boundary'
between computables and non-computables. For one thing, the computer
with its finite arithmetics (due to the fixed number of bits in the
arithmetic units) definitely greatly reduces the computables
from what are 'theoretically' computable in case true real arithmetics
(with infinite precision) were available.

M. K. Shen

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