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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Sat, 15 Mar 2025 14:46:49 -0500
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On 3/15/2025 5:08 AM, Andy Walker wrote:
> On 15/03/2025 01:08, olcott wrote:
>> On 3/14/2025 6:09 PM, Andy Walker wrote:
>>> 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. 
>> Not if GC is true and the proof cannot algorithmically
>> compressed into a finite sequence of steps.
> 
>      You didn't read, or didn't understand, the rest of my article,
> which explains that, indeed, only a finite number of steps is needed.
> Read on before replying:
> 

I always respond to the first mistake.
I did notice that you qualified this later on.


>>>  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/.
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer