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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 18:43:26 -0400
Organization: i2pn2 (i2pn.org)
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On 5/6/25 11:10 AM, olcott wrote:
> On 5/6/2025 4:26 AM, Mikko wrote:
>> On 2025-05-05 18:14:25 +0000, olcott said:
>>
>>> On 5/5/2025 11:16 AM, dbush wrote:
>>>> On 5/5/2025 12:13 PM, Mr Flibble wrote:
>>>>> On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:
>>>>>
>>>>>> On 5/5/2025 11:51 AM, olcott wrote:
>>>>>>> On 5/5/2025 10:17 AM, Mr Flibble wrote:
>>>>>>>> What constitutes halting problem pathological input:
>>>>>>>>
>>>>>>>> Input that would cause infinite recursion when using a decider 
>>>>>>>> of the
>>>>>>>> simulating kind.
>>>>>>>>
>>>>>>>> Such input forms a category error which results in the halting 
>>>>>>>> problem
>>>>>>>> being ill-formed as currently defined.
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> I prefer to look at it as a counter-example that refutes all of the
>>>>>>> halting problem proofs.
>>>>>>
>>>>>> Which start with the assumption that the following mapping is 
>>>>>> computable
>>>>>> and that (in this case) HHH computes it:
>>>>>>
>>>>>>
>>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>>> instructions) X
>>>>>> described as <X> with input Y:
>>>>>>
>>>>>> A solution to the halting problem is an algorithm H that computes the
>>>>>> following mapping:
>>>>>>
>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
>>>>>> directly
>>>>>>
>>>>>>
>>>>>>
>>>>>>> int DD()
>>>>>>> {
>>>>>>>     int Halt_Status = HHH(DD);
>>>>>>>     if (Halt_Status)
>>>>>>>       HERE: goto HERE;
>>>>>>>     return Halt_Status;
>>>>>>> }
>>>>>>>
>>>>>>> https://github.com/plolcott/x86utm
>>>>>>>
>>>>>>> The x86utm operating system includes fully operational HHH and DD.
>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
>>>>>>>
>>>>>>> When HHH computes the mapping from *its input* to the behavior of DD
>>>>>>> emulated by HHH this includes HHH emulating itself emulating DD. 
>>>>>>> This
>>>>>>> matches the infinite recursion behavior pattern.
>>>>>>>
>>>>>>> Thus the Halting Problem's "impossible" input is correctly 
>>>>>>> determined
>>>>>>> to be non-halting.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Which is a contradiction.  Therefore the assumption that the above
>>>>>> mapping is computable is proven false, as Linz and others have proved
>>>>>> and as you have *explicitly* agreed is correct.
>>>>>
>>>>> The category (type) error manifests in all extant halting problem 
>>>>> proofs
>>>>> including Linz.  It is impossible to prove something which is ill- 
>>>>> formed
>>>>> in the first place.
>>>>>
>>>>> /Flibble
>>>>
>>>> All algorithms either halt or do not halt when executed directly. 
>>>> Therefore the problem is not ill formed.
>>>
>>> When BOTH Boolean RETURN VALUES are the wrong answer
>>> THEN THE PROBLEM IS ILL-FORMED. Self-contradiction must
>>> be screened out as semantically incorrect.
>>
>> Irrelevant. One of the boolean values (the one not returned) is the
>> right one as can be determined e.g. with an UTM.
>>
>>>> You only get something that appears that way when a false assumption 
>>>> is made, namely that the halting function is computable.
>>>
>>> The mapping from the input HHH(DD) finite string of
>>> machine code to DOES SPECIFY RECURSIVE EMULATION
>>> THAT WOULD PREVENT DD FROM EVER HALTING.
>>
>> No, it does not. HHH returns 0 and DD halts.
>>
> 
> You can't show the detailed steps of the execution
> trace of DD emulated by HHH (according to the rules
> of the x86 language) where DD halts because you are wrong.

Because a trace of DD correctly emulatd by HHH doesn't exist as HHH 
doesn't correctly emulate DD

> 
> _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]
> 
> 

And by keep on omitting the code of HHH that is part of the input makes 
it seem like you think it itsn't part of the input, in which case you 
problem is even a lie, as you need to give the decider the FULL input, 
not just part of it

I guess you are just trying to see how many ways you can show that you 
are just a liar.