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From: olcott <polcott333@gmail.com>
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 08:20:09 -0500
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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.


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