Re: Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in the Halting Problem

Am Sun, 11 May 2025 18:14:56 -0500 schrieb olcott:

On 5/11/2025 6:05 PM, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

To usefully advance research in this area pathological input needs to
be excluded from the set of programs that can be analysed by a
decider.

 
Can this exclusion be performed reliably and consistently?
 

That is a good question. The answer is definitely yes. When HHH emulates
DDD it only needs to see that DDD is calling itself with no conditional
branch instructions inbetween.

Now that is counter to the facts (besides, DDD doesn't call itself, it
calls a simulator): there is a conditional branch in HHH.

Whether a function computed by a Turing machine can do this is a
different question.

(Mathematical functions don't "do" anything, algorithms do.)
--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.