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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 15:41:59 -0500
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On 5/7/2025 3:24 PM, joes wrote:
> Am Tue, 06 May 2025 13:40:16 -0500 schrieb olcott:
>> On 5/6/2025 10:53 AM, joes wrote:
>>> Am Tue, 06 May 2025 10:29:59 -0500 schrieb olcott:
>>>> On 5/6/2025 4:35 AM, Mikko wrote:
>>>>> On 2025-05-05 17:37:20 +0000, olcott said:
>>>
>>>>>> The above example is category error because it asks HHH(DD) to
>>>>>> report on the direct execution of DD() and the input to HHH
>>>>>> specifies a different sequence of steps.
>>>>>
>>>>> No, it does not. The input is DD specifides exactly the same sequence
>>>>> of steps as DD. HHH just answers about a different sequence of steps
>>>>> instead of the the seqeunce specified by its input.
>>> As agreed to below:
>>>
>>>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>>        If simulating halt decider H correctly simulates its input D
>>>>        until H correctly determines that its simulated D *would never
>>>>        stop running unless aborted* then
>>>>
>>>> *input D* is the actual input *would never stop running unless
>>>> aborted* is the hypothetical H/D pair where H does not abort.
>>
>>> H should simulate its actual input D that calls the aborting H, not a
>>> hypothetical version of D that calls a pure simulator.
>>>
>> *would never stop running unless aborted*
>> refers to the same HHH that DD calls yet this hypothetical HHH does not
>> abort.
> Then it is not the same HHH.
> 

It is the exact same HHH/DD pair except that this
hypothetical HHH never aborts.

>>>> You cannot possibly show the exact execution trace where DD is
>>>> correctly emulated by HHH and this emulated DD reaches past its own
>>>> machine address [0000213c].
>>
>>> Duh, no simulator can simulate itself correctly. But HHH1 can simulate
>>> DD/HHH.
>> HHH does simulate itself correctly yet must create a separate process
>> context for each recursive emulation.
>> Each process context has its own stack and set of virtual registers.

> No, HHH simulates only one program. 

HHH correctly emulates DD and correctly emulates itself
emulating DD. This is two C functions and zero programs.


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