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Date: Sat, 9 Mar 2024 22:59:12 +0100
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On 9/03/24 22:55, olcott wrote:
> On 3/9/2024 3:17 PM, Richard Damon wrote:
>> On 3/9/24 10:33 AM, olcott wrote:
>>> *Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior*
>>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> Specifications, not actual behavior until the existance of such an H 
>> is shown.
>>
>> IF taken as actual behavior, then it is conditional on such an H 
>> existing.
>>
>>>
>>> Execution trace of Ĥ applied to ⟨Ĥ⟩
>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H
>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process
>>> *This proves that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ must abort its simulation*
>>
>> It NEEDS to in order to meet its specification
>>
>> It DOESN'T unless its algorithm says it does,
>>
>> If it just fails to answer, then it has failed to be a correct Halt 
>> Decider.
>>
>> The fact that you reach this conflict in actions, is the reason Halt 
>> Deciding is uncomputable.
>>
>>>
>>> *This is a verified fact*
>>> When simulating halt deciders always report on the behavior of
>>> their simulated input from their own POV then when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>> transitions to Ĥ.Hqn it is correct from its own POV.
>>
>> In other words, you are admitting to changing the question, and thus 
>> LYING that you are working on the actual original problem.
>>
>>>
>>> *This is a verified fact*
>>> When that occurs then H ⟨Ĥ⟩ ⟨Ĥ⟩ would transition to H.qy from
>>> its own POV.
>>
>> Which just means you are LYING that this apply to an actual Halt 
>> Decider per the Halting Theory,
>>
>>>
>>> When Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ report on the basis of their own
>>> POV then Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ reports incorrectly about the behavior of
>>> Ĥ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ reports the behavior of Ĥ ⟨Ĥ⟩ correctly.
>>
>> And thus you are admitting that the H in H^.H is WRONG and thus H is 
>> not a correct Halt Decider, because it gets some cases wrong.
> 
> It is a verified fact that when H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ meet this 
> criteria that H gets the right answer and Ĥ.H gets the wrong answer.

It is a verified fact that it's impossible for H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ 
to both meet this criteria if you honestly followed the Linz proof (for 
Turing machines).

It is a verified fact that it's impossible for H ⟨Ĥ⟩ ⟨Ĥ⟩ <H> and Ĥ.H ⟨Ĥ⟩ 
⟨Ĥ⟩ <H> to both meet this criteria if you honestly followed the modified 
Linz proof (for Olcott machines).