Re: Every sufficiently competent C programmer knows --- Semantic Property of Finite String

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.]