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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Computable Functions --- finite string transformation rules
Date: Thu, 24 Apr 2025 19:07:49 -0400
Organization: i2pn2 (i2pn.org)
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On 4/24/25 3:41 PM, olcott wrote:
> On 4/24/2025 2:12 PM, Fred. Zwarts wrote:
>> Op 24.apr.2025 om 19:13 schreef olcott:
>>>
>>> HHH correctly determines through mathematical induction that
>>> DD emulated by HHH (according to the finite string transformations
>>> specified by the x86 language) cannot possibly reach its final
>>> halt state in an infinite number of steps.
> 
>> No, HHH has a bug which makes that it fails to see that there is only 
>> a finite recursion, 
> 
> *You are technically incompetent on this point*
> When the finite string transformation rules of the
> x86 language are applied to the input to HHH(DD)
> THIS DD CANNOT POSSIBLY REACH ITS FINAL HALT STATE
> not even after an infinite number of emulated steps.

When the defined finite string trasnsformation rules, thos of the x86 
language, are applied to this input, completed with the definitions from 
Halt7.c as stipulated, we see that DD calls HHH(DD), that it will spend 
some time emulating DDm then it will give up and return 0 to DD which 
will then halt.

THe fact that HHH doesn't complete this operation, doesn't mean that it 
isn't what the x86 language says will happen, just that HHH doesn't know 
that is what happens.

THus, HHH just fails to know what to do, and because you were so stupid 
as to program it with unsound logic, it gets that wrong answer.

Your problem is you confuse the partial, and thus INCORRECT emulatation 
done by HHH with the correct and complete emulation specified by the x86 
language and the full input which includes the code of HHH from Halt7.c

> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> _DD()
> [00002133] 55         push ebp      ; housekeeping
> [00002134] 8bec       mov ebp,esp   ; housekeeping
> [00002136] 51         push ecx      ; make space for local
> [00002137] 6833210000 push 00002133 ; push DD
> [0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
> [00002141] 83c404     add esp,+04
> [00002144] 8945fc     mov [ebp-04],eax
> [00002147] 837dfc00   cmp dword [ebp-04],+00
> [0000214b] 7402       jz 0000214f
> [0000214d] ebfe       jmp 0000214d
> [0000214f] 8b45fc     mov eax,[ebp-04]
> [00002152] 8be5       mov esp,ebp
> [00002154] 5d         pop ebp
> [00002155] c3         ret
> Size in bytes:(0035) [00002155]
> 
> 
> 
>