Re: Bad faith and dishonesty

On 30/05/2025 10:19, vallor wrote:

On Thu, 29 May 2025 19:40:57 +0100, Richard Heathfield <rjh@cpax.org.uk>
wrote in <101a9np$gl7$1@dont-email.me>:
 

On 29/05/2025 19:14, olcott wrote:

<snip>

>
It is a tautology that any input D to termination analyzer H that
*would never stop running unless aborted*
DOES SPECIFY NON-TERMINATING BEHAVIOR.

>
But in making that claim you assume that you correctly know the
termination behaviour of D.
>
I can easily sketch out a program that your HHH analyser would
impatiently abort as non-terminating, but which could conceivably stop
running this year, next year, sometime... or never.

 Was wondering when someone would mention that...what does his HHH()
do with arbitrary programs?
 $ cat ddd.c
#include <stdio.h>
 void ddd(int r)
     {
     r--;
     if(r <= 0) return;
     fprintf(stderr,"calling ddd(%d)\n",r);
     ddd(r);
     fprintf(stderr,"returning, r=%d\n",r);
     return;
     }
  int main(void)
{
 ddd(50);
 return 0;
}
 I'd bet his HHH() would say this is non-terminating.

Dunno. I can't test it because I was unable to construct his system locally, but your program terminates quite quickly, so maybe he can cope with it? I'm not sure.
Here's a sketch of a rather more ambitious program that will definitely give his HHH some serious pause for thought.
Imagine if you will a bignum library that can cope with basic arithmetic on integers whose bit patterns are stored in arbitrarily large arrays of unsigned char. (I have written such a library for my own purposes, but you could use Miracl or GMP.)
Clearly, in C this would be implemented using function calls, but for the sake of brevity in my sketch I'll pretend that C has operator overloading.
You could use the bignum library to implement Miller-Rabin, which I'll call is_prime().
Given all of this, we can sketch out a design for a C program that can't prove, but may or may not DISprove, the Goldbach conjecture:
int main(void)
{
   int found = 0;
   bignum even = 4;
   while(!found)
   {
     even += 2;
     found = check(even);
   }
   if(found)
   {
     printf("Goldbach conjecture is FALSE."
            " Pass me a Fields Medal.\n");
   }
   return EXIT_SUCCESS;
}
int check(bignum n)
{
   int found = 1; /* assume n is a counterexample */
   bignum i, j;
   for(i = 3; found && i += 2; i++)
   {
     j = n - i;
     if(is_prime(i) && is_prime(j))
     {
       /* n is NOT a counter-example */
       found = 0;
     }
   }
   return found;
}
Good luck with that, HHH().
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within