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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: =?utf-8?Q?Re:_A_simulating_halt_decider_applied_to_the_The_Peter_Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
Date: Fri, 31 May 2024 16:00:44 +0300
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On 2024-05-30 13:20:09 +0000, olcott said:

> On 5/30/2024 2:06 AM, Mikko wrote:
>> On 2024-05-29 13:13:13 +0000, olcott said:
>> 
>>> On 5/29/2024 3:37 AM, Mikko wrote:
>>>> On 2024-05-28 11:34:24 +0000, Richard Damon said:
>>>> 
>>>>> On 5/27/24 10:59 PM, olcott wrote:
>>>>>> On 5/27/2024 9:52 PM, Richard Damon wrote:
>>>>>>> On 5/27/24 10:41 PM, olcott wrote:
>>>>>>>> On 5/27/2024 9:23 PM, Richard Damon wrote:
>>>>>>>>> On 5/27/24 10:01 PM, olcott wrote:
>>>>>>>>>> On 5/27/2024 8:24 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/27/24 9:04 PM, olcott wrote:
>>>>>>>>>> 
>>>>>>>>>>>>>> I totally do. Can you please write down the
>>>>>>>>>>>>>> "completely specified state transition/tape operation table."
>>>>>>>>>>>>>> of this specific (thus uniquely identifiable) machine I would
>>>>>>>>>>>>>> really like to see it.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>> 
>>>>>>>>>>>>> But it was proven that no such machine exists!
>>>>>>>>>>>>> 
>>>>>>>>>>>>> Remember, the proof starts with the hypothetical that such a machine 
>>>>>>>>>>>>> exists. Such a machine WOULD HAVE a completely specified state 
>>>>>>>>>>>>> transition/tape operation table.
>>>>>>>>>>>>> 
>>>>>>>>>>>> 
>>>>>>>>>>>> That is not what you said.
>>>>>>>>>>>>  >>>>> There doesn't need to be a unique finite string, but it is a 100%
>>>>>>>>>>>>  >>>>> completely specified state transition/tape operation table.
>>>>>>>>>>>> 
>>>>>>>>>>>> "a 100% completely specified state transition/tape operation table"
>>>>>>>>>>>> of a non-existent machine.
>>>>>>>>>>> 
>>>>>>>>>>> Right, by presuming that you have a Turing Machine, you have a 
>>>>>>>>>>> completly specified state transition/tape operation table.
>>>>>>>>>>> 
>>>>>>>>>>> You may not KNOW what that table is if you don't know what the exact 
>>>>>>>>>>> machine is, but you know it exists.
>>>>>>>>>> 
>>>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>>>  > ... but you know it exists.
>>>>>>>>>> 
>>>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>>>  > ... but you know it exists.
>>>>>>>>>> 
>>>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>>>  > ... but you know it exists.
>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> Really, then show that one exists!
>>>>>>>>> 
>>>>>>>> 
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> Really, where did I say that H exists?
>>>>>>> 
>>>>>>> I said that if a Turing Machine exists, then its transition table does too.
>>>>>>> 
>>>>>> 
>>>>>> OK my mistake this time. I did not take into account the full context.
>>>>>> I will go back an read the Linz proof and see if he said anything
>>>>>> about a specific machine.
>>>>> 
>>>>> Read the DEFINITION of the problem. He talks about "a" machine. Using a 
>>>>> singular article means you are working with just one.
>>>>> 
>>>>> 
>>>>> Taking stuff out of context is a common problem with you, when you 
>>>>> don't understand something, you just make up what it must mean, and 
>>>>> stick to that. That isn't the way to learn.
>>>>> 
>>>>> 
>>>>>> 
>>>>>> None of the proofs ever try to show that there exists one machine that
>>>>>> gets the wrong answer. They are always at least trying to prove that no
>>>>>> machine of the infinite set of machine gets the right answer.
>>>>>> 
>>>>> 
>>>>> What I see, is they always start with a prototypical single machine, 
>>>>> and show that it gets the answer wrong, and then they use categorical 
>>>>> logic to say that we can do this same thing for all of them.
>>>> 
>>>> It is possible to formulate the claim and proof so that H is an universally
>>>> quantified variable. But the usual way is apparently equally good for the
>>>> target audience.
>>>> 
>>> 
>>> *Formalizing the Linz Proof structure*
>>> ∃H  ∈ Turing_Machines
>>> ∀x  ∈ Turing_Machines_Descriptions
>>> ∀y  ∈ Finite_Strings
>>> such that H(x,y) = Halts(x,y)
>> 
>> That is not a proof structure. That is the counter-hypothesis of Linz' proof.
>> Also note that both x and y are finite strings.
>> 
> 
> The above is what Linz is claiming evaluates to false, he says
> there is no such H.

Yes, and proves the claim.

> A decider computes the mapping from finite string inputs to
> its own accept or reject state.

An existing decider.

> A decider does not and cannot compute the mapping from Turing_Machine
> inputs to its own accept or reject state.

An exsiting decider.

-- 
Mikko