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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?B?ZW1iZWRkZWRfSCBhcHBsaWVkIHRvIOKfqMSk4p+pIOKfqMSk4p+p?=
Date: Mon, 29 Jul 2024 11:16:13 -0500
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On 7/28/2024 3:02 AM, Mikko wrote:
> On 2024-07-27 14:08:10 +0000, olcott said:
> 
>> On 7/27/2024 2:21 AM, Mikko wrote:
>>> On 2024-07-26 14:08:11 +0000, olcott said:
>>>
>>>> On 7/26/2024 3:45 AM, Mikko wrote:
>>>>> On 2024-07-24 13:33:55 +0000, olcott said:
>>>>>
>>>>>> On 7/24/2024 3:57 AM, Mikko wrote:
>>>>>>> On 2024-07-23 13:31:35 +0000, olcott said:
>>>>>>>
>>>>>>>> On 7/23/2024 1:32 AM, 0 wrote:
>>>>>>>>> On 2024-07-22 13:46:21 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 7/22/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>> On 2024-07-21 13:34:40 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> On 7/21/2024 4:34 AM, Mikko wrote:
>>>>>>>>>>>>> On 2024-07-20 13:11:03 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2024-07-19 14:08:24 +0000, olcott said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> When we use your incorrect reasoning we would conclude
>>>>>>>>>>>>>>>> that Infinite_Loop() is not an infinite loop because it
>>>>>>>>>>>>>>>> only repeats until aborted and is aborted.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You and your HHH can reason or at least conclude 
>>>>>>>>>>>>>>> correctly about
>>>>>>>>>>>>>>> Infinite_Loop but not about DDD. Possibly because it 
>>>>>>>>>>>>>>> prefers to
>>>>>>>>>>>>>>> say "no", which is correct about Infinte_loop but not 
>>>>>>>>>>>>>>> about DDD.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Because this is true I don't understand how you are not 
>>>>>>>>>>>>>> simply lying*
>>>>>>>>>>>>>> int main
>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>    DDD();
>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Calls HHH(DDD) that must abort the emulation of its input
>>>>>>>>>>>>>> or {HHH, emulated DDD and executed DDD} never stop running.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You are the lying one.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If HHH(DDD) abrots its simulation and returns true it is 
>>>>>>>>>>>>> correct as a
>>>>>>>>>>>>> halt decider for DDD really halts.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> (b) We know that a decider is not allowed to report on the 
>>>>>>>>>>>> behavior
>>>>>>>>>>>> computation that itself is contained within.
>>>>>>>>>>>
>>>>>>>>>>> No, we don't. There is no such prohibition.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Turing machines never take actual Turing machines as inputs.
>>>>>>>>>> They only take finite strings as inputs and an actual executing
>>>>>>>>>> Turing machine is not itself a finite string.
>>>>>>>>>
>>>>>>>>> The definition of a Turing machine does not say that a Turing 
>>>>>>>>> machine
>>>>>>>>> is not a finite string. It is an abstract mathematical object 
>>>>>>>>> without
>>>>>>>>> a specification of its exact nature. It could be a set or a finite
>>>>>>>>> string. Its exact nature is not relevant to the theory of 
>>>>>>>>> computation,
>>>>>>>>> which only cares about certain properties of Turing machines.
>>>>>>>>>
>>>>>>>>>> Therefore It is not allowed to report on its own behavior.
>>>>>>>>>
>>>>>>>>> Anyway, that does not follow. The theory of Turing machines 
>>>>>>>>> does not
>>>>>>>>> prohibit anything.
>>>>>>>>>
>>>>>>>>>> Another different TM can take the TM description of this
>>>>>>>>>> machine and thus accurately report on its actual behavior.
>>>>>>>>>
>>>>>>>>> If a Turing machine can take a description of a TM as its input
>>>>>>>>> or as a part of its input it can also take its own description.
>>>>>>>>> Every Turing machine can be given its own description as input
>>>>>>>>> but a Turing machine may interprete it as something else.
>>>>>>>>>
>>>>>>>> In this case we have two x86utm machines that are identical
>>>>>>>> except that DDD calls HHH and DDD does not call HHH1.
>>>>>>>
>>>>>>> That DDD calls HHH and DDD does not call HHH1 is not a difference
>>>>>>> between two unnamed turing machines.
>>>>>>>
>>>>>>
>>>>>> The same thing happens at the Peter Linz Turing Machine level
>>>>>> I will provide that more difficult example if and only if you
>>>>>> prove that you understand this one.
>>>>>
>>>>> However, Peter Linz does not call taht same thing a difference.
>>>>
>>>> We can call everything "late for dinner" with a unique integer
>>>> index and the properties that I assert exist still exist.
>>>
>>> That you can say all sorts stupid things does not mean that it be a
>>> good idea to do so.
>>>
>>> Some of the properties you assert exsit actually do exist, some don't.
>>>
>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>
>>
>> The above is merely simplified syntax for the top of page 3
>> https://www.liarparadox.org/Linz_Proof.pdf
>> The above is the whole original Linz proof.
> 
> And even more simplified semantics.
> 
>> (a) Ĥ copies its input ⟨Ĥ⟩
>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>> (g) goto (d) with one more level of simulation
>>
>> You are supposed to evaluate the above as a contiguous
>> sequence of moves such that non-halting behavior is
>> identified.
> 
> The above is an obvious tight loop of (d), (e), (f), and (g).
> Its relevance (it any) to the topic of the discussion is not
> obvious.
> 

When we compute the mapping from the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
to the behavior specified by this input we know that embedded_H
is correct to transition to Ĥ.qn.

Everyone say no, no that it not the behavior of the computation
that embedded_H is contained within: Ĥ applied to ⟨Ĥ⟩.

It is not supposed to be (or allowed to be) the behavior
of the executing Turing machine that embedded_H is contained
within.

It is only supposed to be the behavior that the input to
embedded_H specifies and this includes recursive simulation.


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