Re: Computable Functions --- finite string transformation rules

Am Fri, 25 Apr 2025 16:21:30 -0500 schrieb olcott:

On 4/25/2025 8:56 AM, joes wrote:

Am Thu, 24 Apr 2025 19:03:34 -0500 schrieb olcott:

Mathematical induction proves that DD emulated by HHH cannot possibly
reach its own final state in an infinite number of steps and it does
this with one recursive emulation.
There is a repeating pattern that every C programmer can see.

 

Like Fred wrote months ago, that has nothing to do with the
contradictory part of DD,

Sure it does. The contradictory part of DD has always been unreachable
thus only a ruse.

Then it can't be due to that. It even works with HHH(HHH)!

only with it being simulated by the same simulator it calls.

That <is> the Halting Problem counter-example input.

This is not, but behaves the same:

The program EE(){ HHH(EE); } also halts and cannot be simulated by HHH.
 

HHH cannot possibly do this without violating the rules of the x86
language.
The finite string transformation rules of the x86 language applied to
the input to HHH(DD) only correctly derive not halting.

No, the rules applied to DD (which is the input to HHH) derive "halting",
but HHH is like any simulator incapable of simulating itself to
completion.

--
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.