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From: olcott <polcott333@gmail.com>
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 15:15:32 -0500
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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!

> and the next H, so the 
> simulated H never reaches its abort, and therefore it does not reach its 
> final state. D acts only as a quick parameter duplicator so that H 
> simulates itself. Then simulated H gets stuck in an infinite recursion 
> and never reaches the 'pathological' part of D.
> Even a beginning C programmer will see that if the simulated H would 
> really halt (as required), 

It does yet you continue to fail to understand this.

> then simulated D would continue to line 04.

No that is utterly impossible because the only reason
that H halts is that it totally stops simulating D.

> But simulated H does not halt and must be aborted.
> 
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer