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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
 =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
Date: Thu, 30 May 2024 21:37:36 -0400
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On 5/30/24 9:20 AM, olcott wrote:
> 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.
> 
> 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.
> 
> 

Then I guess you are admititng as a matter of definition that no Turing 
machine can be a Halt Decider, since BY THE DEFINITON of a Halt Decider, 
that you have even quoted, it can't consider that as a proper input.

Remember, a Halt Decider is to decide if the Turing Machine described by 
the input will halt. If it is impossible to compute a mapping about a 
Turing Machine described by the input, then Halt Deciding in just 
impossible.