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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Mike Terry Proves --- How the requirements that Professor Sipser agreed to are exactly met
Date: Tue, 20 May 2025 10:00:21 +0300
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On 2025-05-20 04:10:54 +0000, olcott said:

> On 5/19/2025 5:12 AM, Mikko wrote:
>> On 2025-05-18 19:18:21 +0000, olcott said:
>> 
>>> On 5/18/2025 2:08 PM, joes wrote:
>>>> Am Sun, 18 May 2025 12:28:05 -0500 schrieb olcott:
>>>>> On 5/18/2025 10:21 AM, Mike Terry wrote:
>>>>>> On 18/05/2025 10:09, Mikko wrote:
>>>>>>> On 2025-05-17 17:15:14 +0000, olcott said:
>>>> 
>>>>>>>> HHH(DDD) does not base its decision on the actual behavior of DDD
>>>>>>>> after it has aborted its simulation of DDD, instead it bases its
>>>>>>>> decision on a different HHH/DDD pair that never aborts.
>>>>>>> 
>>>>>>> This is why HHH does not satisfy "H correctly determines that its
>>>>>>> simulated D would never stop running unless aborted". If HHH bases its
>>>>>>> decision on anything else than what its actual input actually
>>>>>>> specifies it does not decide correctly.
>>>>>>> 
>>>>>> Right.  It seems to be a recent innovation in PO's wording that he has
>>>>>> started using the phrase "..bases its decision on a different *HHH/DDD
>>>>>> pair* ..".
>>>>>> 
>>>>> Thus SHD must report on a different SHD/Infinite_Loop pair where this
>>>>> hypothetical instance of itself never aborts.
>>>> This, the simulator. The input still calls the same real aborting HHH.
>>>> 
>>>>> If H always reports on the behavior of its simulated input after it
>>>>> aborts then every input including infinite_loop would be determined to
>>>>> be halting.
>>>> Yes, that is why H is wrong.
>>>> 
>>>>> Instead H must report on the hypothetical H/D input pair where the very
>>>>> same H has been made to not abort its input.
>>>> Just no.
>>>> 
>>>>> *H correctly determines that its simulated D*
>>>>> *would never stop running unless aborted*
>>>>> by a hypothetical instance of itself that never aborts.
>>>> H does stop running when simulated without aborting, because it aborts.
>>>> 
>>> 
>>> H is required to report on the behavior of D in the
>>> case where a hypothetical instance of itself never
>>> aborts its simulated D.
>>> 
>>> When the hypothetical H never aborts its simulated D then:
>>> (a) Simulated D  NEVER HALTS
>>> (b) Executed D() NEVER HALTS
>>> (c) Executed H() NEVER HALTS
>>> (d) Everything that H calls NEVER HALTS
>> 
>> You forgot
>> (e) H does not report
> 
> HHH is required to report, that is why it
> must always report on the behavior of the
> hypothetical H/D pair and not the actual
> behavior of the actual H/D pair for every
> non-terminating input.

Every decider is required to report. But your (c) above prevents the
hypothetical H from reporting. Therefore the hypothetical H is not a
decider.

-- 
Mikko