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From: immibis <news@immibis.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Refutation of the Peter Linz Halting Problem proof 2024-03-05
 --partial agreement--
Date: Sat, 9 Mar 2024 16:33:29 +0100
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On 9/03/24 16:04, olcott wrote:
> On 3/9/2024 7:11 AM, immibis wrote:
>> On 8/03/24 20:08, olcott wrote:
>>> On 3/8/2024 12:58 PM, immibis wrote:
>>>> On 8/03/24 19:12, olcott wrote:
>>>>>
>>>>> Unless it is an extra parameter it has no basis for doing this.
>>>>> If it is an extra parameter then it is no longer the Linz proof.
>>>>>
>>>>
>>>> So it's impossible to make a Turing machine that writes 12345 onto 
>>>> its tape unless 12345 is a parameter?
>>>
>>> That is a valid point.
>>> It is impossible to get me to talk about that until
>>> we first have full closure that the Linz H correctly
>>> determines the halt status of the Linz Ĥ ⟨Ĥ⟩ when run
>>> in the Olcott master UTM.
>>>
>>
>> When run in the Olcott master UTM as Olcott machines, the Linz proof 
>> does not work because it is designed for Turing machines. A different 
>> proof works.
> 
> Because Olcott machines are more powerful than Turing Machines they can 
> correctly determine the halt status of this input: H ⟨Ĥ⟩ ⟨Ĥ⟩ <H>.
> 

Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <H> always calculates the same answer that H ⟨Ĥ⟩ ⟨Ĥ⟩ <H> 
calculates.