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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is Correctly rejected as
 non-halting V2
Date: Sat, 27 Jul 2024 09:08:10 -0500
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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.


(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.

Two complete simulations (provided above) show a pair of
identical TMD's are simulating a pair of identical inputs.
We can see this thus proving recursive simulation.

The one key thing that I add to the original Linz proof
is that embedded_H computes the mapping from ⟨Ĥ⟩ ⟨Ĥ⟩
finite strings to the behavior that those strings specify.

embedded_H does this as if it was a UTM that can simulate
itself simulating ⟨Ĥ⟩ ⟨Ĥ⟩.

 From the non-terminating behavior pattern that we can see
in (a) through (g) we know that embedded_H can abort its
simulation and reject its input finite strings.

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