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From: Andy Walker <anw@cuboid.co.uk>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Fri, 14 Mar 2025 23:09:53 +0000
Organization: Not very much
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On 14/03/2025 19:48, Keith Thompson wrote:
> [...] That would imply that [PO] could solve
> Goldbach's Conjecture, among other things, but I haven't seen him
> do so.

	Perhaps [just about] worth noting that a sufficiently long
[but not "infinite"] brute force attack on the GC [and many other
similar conjectures] would resolve the issue.  Basically, if you
have a program [eg, TM] of size N by some suitable measure [eg, TM
states] then within [eg] BB(N) steps it must find the counter-example
[if there is one] or else there isn't one [and the GC is proven true],
where BB is the Busy Beaver function.  Of course, BB is uncomputable,
but that doesn't mean specific individual values are uncomputable,
just that there is no TM that computes it /in general/.

	[I have mentioned here before that BB gives us a much less
troublesome way of attacking the HP than the standard proofs.]

-- 
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Mayer