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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs --- MT
Date: Tue, 6 May 2025 20:25:36 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Tue, 06 May 2025 12:49:13 -0500 schrieb olcott:
> On 5/6/2025 6:23 AM, Richard Damon wrote:
>> On 5/5/25 10:36 PM, olcott wrote:
>>> On 5/5/2025 8:23 PM, Richard Damon wrote:
>>>> On 5/4/25 9:23 PM, olcott wrote:
>>>>> On 5/4/2025 8:04 PM, Ben Bacarisse wrote:
>>>>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>>>> ...
>>>>>>> As explained above, UTM(⟨Ĥ⟩ ⟨Ĥ⟩) simulates Ĥ run with input Ĥ
>>>>>>> (having the same halting behaviour) and Ĥ run with input Ĥ HALTS. 
>>>>>>> So embedded_H does not "gather enough information to deduce that
>>>>>>> UTM(⟨Ĥ⟩ ⟨Ĥ⟩) would never halt".  THAT IS JUST A FANTASY THAT YOU
>>>>>>> HAVE.
>>>>>>> UTM(⟨Ĥ⟩ ⟨Ĥ⟩) DOES halt, so embedded_H can't possibly gather
>>>>>>> information that genuinely implies it DOESN'T halt.  The
>>>>>>> explanation is obvious: embedded_H gathers information that *YOU*
>>>>>>> believe implies that UTM(⟨Ĥ⟩ ⟨Ĥ⟩)
>>>>>>> would never halt, but *YOU ARE SIMPLY WRONG*.
>>>>>>
>>>>>> He used to claim that false ("does not halt") was the correct
>>>>>> answer,
>>>>>> /even though/ the computation in question halts!  Those were
>>>>>> simpler days.  Of course cranks will never admit to having been
>>>>>> wrong about anything other than a detail or two, so anyone who
>>>>>> could be bothered could try to get him to retract that old claim.
>>>>>>
>>>>> <MIT Professor Sipser agreed to ONLY these verbatim words
>>>>> 10/13/2022>
>>>>> </MIT Professor Sipser agreed to ONLY these verbatim words
>>>>> 10/13/2022>
>>>>>
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> In other words embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct to reject its input if
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn Would not halt.
>>>>
>>>> Nope, because that isn't the input that it was given.
>>>
>>> *Wrong*
>>> <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
>>>
>>> *simulated D would never stop running unless aborted*
>>> simulated D (the actual input)
>>> never stop running unless aborted (hypothetical H/D pair)
>>>
>> No, that is changing the input.
>> 
> *would never stop running unless aborted* means the hypothetical same
> HHH that DD calls except that this HHH does not abort.
Yes, that is not the same HHH.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.