Infinite length computer programs

From: Russell Standish <R.Standish.domain.name.hidden>
Date: Mon, 26 May 2003 09:19:36 +1000 (EST)

Before this thing gets totally out of context, may I remind
participants that we are talking about infinite length strings called
"descriptions" in the Schmidhuber ensemble. These descriptions may be
fed into a Turing Machine, where they become programs. There is a 1-1
correspondence between these and real numbers, as can be seen by
expanding real numbers in binary expansion.

The more usual program we're used to is of finite length, and
corresponds to a set of infinite length programs having the same
prefix. These sets have positive measure 2^{-\ell} where \ell is the
length of the program.

                                                Cheers

Jean-Michel Veuillen wrote:
> >This is where we make closest contact. There are an uncountable
> >infinity of factorial programs written in Fortran.
>
> I can spot a mistake here: There is a one to one correspondance between
> computer programs and integers. Think of a computer program as another way
> of writing an integer, in another base.
>
> Jean-Michel Veuillen
>



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Received on Sun May 25 2003 - 19:24:04 PDT

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