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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets --- deciders
Date: Thu, 30 May 2024 22:59:12 +0200
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Op 30.mei.2024 om 22:15 schreef olcott:
> On 5/30/2024 2:32 PM, Fred. Zwarts wrote:
>> Op 30.mei.2024 om 21:01 schreef olcott:
>>> On 5/30/2024 1:50 PM, Fred. Zwarts wrote:
>>>> Op 30.mei.2024 om 19:00 schreef olcott:
>>>>> On 5/30/2024 10:20 AM, Fred. Zwarts wrote:
>>>>>> Op 30.mei.2024 om 16:43 schreef olcott:
>>>>>>> On 5/28/2024 11:16 AM, olcott wrote:
>>>>>>>>
>>>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>
>>>>>>>> *Formalizing the Linz Proof structure*
>>>>>>>> ∃H  ∈ Turing_Machines
>>>>>>>> ∀x  ∈ Turing_Machines_Descriptions
>>>>>>>> ∀y  ∈ Finite_Strings
>>>>>>>> such that H(x,y) = Halts(x,y)
>>>>>>>>
>>>>>>>
>>>>>>> A decider computes the mapping from finite string inputs to
>>>>>>> its own accept or reject state.
>>>>>>>
>>>>>>> A decider does not and cannot compute the mapping from
>>>>>>> Turing_Machine inputs to its own accept or reject state.
>>>>>>>
>>>>>>> Halts(x,y) would report on the direct execution of x(y) thus ignores
>>>>>>> the pathological behavior of x correctly simulated by pure 
>>>>>>> function H.
>>>>>>> This makes Halts(x,y) an incorrect measure of the correctness of 
>>>>>>> H(x,y).
>>>>>>
>>>>>> Why are you referring to the 'pathological behavior of x' if your 
>>>>>> claim is that the simulator does not even reach the part of DD 
>>>>>> (below) that contradicts the result of HH? This 'pathological 
>>>>>> behavior of x' is completely irrelevant. 
>>>>>
>>>>> It is totally relevant because it is the reason why D correctly
>>>>> simulated by H cannot possibly halt.
>>>>
>>>> Incorrect. Your own words are that lines 04, 05 and 06 are nor 
>>>> reachable for the simulator.
>>>
>>> Because D correctly simulated by H remains stuck in recursive simulation
>>> because D calls H(D,D) in recursive simulation D cannot possibly reach
>>> past its own line 03.
>>>
>>> You must must 100% complete attention to the exact words that I 
>>> exactly say.
>>>
>>
>> If you ask to 100% attention, please, pay also attention to the 
>> replies and read more than the first few words. You remove most of my 
>> reply, probably because you did not read them.
>>
> 
> I soon as yo show that you are starting with a fundamentally false 
> assumption I stop reading.
> 
>> The fact that D does not reach past line 03, means that lines 04, 05 
>> and 06 do not play a role in the decision.
> 
> OK
> 
>> Do you understand C? 
> 
> I learned C back when K&R was the standard and have been a professional
> C++ software engineer for two decades. I have been professional
> programmer since 1984.
> 
>> If line 04 cannot be reached, lines 05 and 06 do not cause any 
>> behaviour. In particular no 'pathological' behaviour.
>>
> 
> The reason why these lines can't be reached is that D calls H(D,D)
> in recursive simulation. This relationship between H and D is
> typically called pathological.
> 
>> It is H that keeps repeating the simulation of D 
> 
> D calls H(D,D) in recursive simulation until H stops this.
> THIS IS D'S FAULT!

Shouting does not make it true! It shows a lack of reasoning.

This is a fundamentally false assumption, so I stop reading here.
It is not D's fault. It is H's choice to start the simulation, not D's. 
D does not even know of simulation at all. D is assumed to call a 
decider that is required to halt, so it is H's task to halt the decision 
process, not D's. But H fails to halt: H keeps simulating H in recursive 
simulation, but if the simulation of H would halt (that is a 
requirement), then D would continue with line 04. Every competent C 
programmer can see that. But the simulation of H violates that requirement.

The fact that H gets stuck in recursive simulation is inherent to a 
simulating halt decider. That makes a simulating halt decider a bad idea.