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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 07:06:38 -0400
Organization: i2pn2 (i2pn.org)
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On 5/5/25 10:29 PM, olcott wrote:
> On 5/5/2025 8:06 PM, Richard Damon wrote:
>> On 5/5/25 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.
>>>
>>> int DD()
>>> {
>>>    int Halt_Status = HHH(DD);
>>>    if (Halt_Status)
>>>      HERE: goto HERE;
>>>    return Halt_Status;
>>> }
>>
>> Which isn't a program until you include the SPECIFIC HHH that it 
>> refutes, and thus your talk about correctly emulated by HHH is just a 
>> lie.
>>
>>>
>>> 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.
>>>
>>
>> And *ITS INPUT*, for the HHH that answers 0, is the representation of 
>> a program 
> 
> Not at all. This has always been stupidly wrong.
> The input is actually a 100% perfectly precise
> sequence of steps. With pathological self-reference
> some of these steps are inside the termination analyzer.
> 

Can't be, as the input needs to be about a program, which must, by the 
definition of a program, include all its algorithm.

Yes, there are steps that also occur in the termination analyzer, but 
they have been effectively copied into the program the input describes.

Note, nothing says that the representation of the program has to be an 
assembly level description of it. It has to be a complete description, 
that 100% defines the results the code will generate (and if it will 
generate) but it doesn't need to be the exact assembly code,

YOU even understand that, as you present the code as "C" code, which 
isn't assembly.

What you forget is that the input program INCLUDES as its definiton, all 
of the code it uses, and thus the call to the decider it is built on 
includes that code into the decider, and that is a FIXED and DETERMINDED 
version of the decider, the one that THIS version of the input is 
designed to make wrong.

This doesn't change when you hypothosize a different decider looking at 
THIS input.