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From: Juergen Schmidhuber <juergen.domain.name.hidden>

Date: Thu, 4 Nov 1999 09:33:36 +0100

Bruno:

*>But in that case Schmidhuber generates also only rationnal approximation
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*>of the computable real number he is generating.
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*>I am not looking at the output of a process (nor is Schmidhuber), I am
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*>looking at the limit of that process after a countable time.
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*>So I insist, by admitting a countable time (not something which I get
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*>at any step) the dovetailing on the initial segments (which of course are
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*>just rationnals) gives a procedure dovetailing on ALL the reals.
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In countably infinite time you can compute an entire real, but not

all reals.

Hal:

*>> The precise probabilities are never really computed.
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*>....Approximate probabilities based on approximations to the
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*>K. complexity of a string are no more computable than precise ones.
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*>There is no fixed bound B which allows you to compute the K. complexity
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*>of an arbitrary string within accuracy B.
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You should add "within a given fixed time interval." Within finite

(though unknown) time you can compute the K of finite string x. In

general you'll just never know whether your current lowest upper bound

on K is tight.

Juergen www.idsia.ch

Received on Thu Nov 04 1999 - 01:06:34 PST

Date: Thu, 4 Nov 1999 09:33:36 +0100

Bruno:

In countably infinite time you can compute an entire real, but not

all reals.

Hal:

You should add "within a given fixed time interval." Within finite

(though unknown) time you can compute the K of finite string x. In

general you'll just never know whether your current lowest upper bound

on K is tight.

Juergen www.idsia.ch

Received on Thu Nov 04 1999 - 01:06:34 PST

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