Re: *THE* PUZZLE (was: ascension, Smullyan, ...)

From: Russell Standish <r.standish.domain.name.hidden>
Date: Thu, 8 Jun 2006 15:49:49 +1000

On Thu, Jun 08, 2006 at 04:24:51AM +0200, Quentin Anciaux wrote:
>
> Le Jeudi 8 Juin 2006 02:56, Russell Standish a écrit :
> > On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
> > > Hi Bruno,
> > >
> > > what I undestand about the UD is that it generates all programs, a
> > > program being simply a number from the set N.(1)
> >
> > No - halting programs are a subset of N, but there are uncountably
> > infinite non-halting ones.
>
> Do you mean there exists programs which are not encodable in a finite string ?
> Is this really a "program" then ? And I see plenty of non-halting program
> which are perfectly writeable in a few instruction.
>

Of course there are finite length non-halting programs. The question
is whether infinite length input tapes are considered programs - isn't
this as much a matter of definition than anything else?

We can distinguish between those tapes that cause a finite number of
symbols to be read from the tape (including all halting programs) from those
tapes that do not (when fed an infinite tape).

> > (Assuming we identify all programs without taking the non-read bits
> > into account).
>
>

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Received on Thu Jun 08 2006 - 01:50:53 PDT