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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: HHH maps its input to the behavior specified by it --- key error
 in all the proofs
Date: Mon, 12 Aug 2024 07:43:30 -0500
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On 8/11/2024 12:06 PM, Richard Damon wrote:
> On 8/11/24 8:40 AM, olcott wrote:
>> On 8/11/2024 6:08 AM, Richard Damon wrote:
>>> On 8/10/24 10:38 PM, olcott wrote:
>>>> On 8/10/2024 9:21 PM, Richard Damon wrote:
>>>>> On 8/10/24 9:43 PM, olcott wrote:
>>>>>> On 8/10/2024 8:13 PM, Richard Damon wrote:
>>>>>>> On 8/10/24 8:51 PM, olcott wrote:
>>>>>>>> On 8/10/2024 7:20 PM, Richard Damon wrote:
>>>>>>>>> On 8/10/24 7:52 PM, olcott wrote:
>>>>>>>>>> On 8/10/2024 5:47 PM, Richard Damon wrote:
>>>>>>>>>>> On 8/10/24 6:41 PM, olcott wrote:
>>>>>>>>>>>> On 8/10/2024 4:53 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 8/10/24 5:37 PM, olcott wrote:
>>>>>>>>>>>>>> On 8/10/2024 4:33 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 8/10/24 5:18 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 8/10/2024 3:58 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 8/10/24 4:36 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> As I have countlessly proven it only requires enough 
>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>> emulated steps to correctly infer that the input would 
>>>>>>>>>>>>>>>>>> never
>>>>>>>>>>>>>>>>>> reach is "return" instruction halt state.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Except that HHH does't do that, since if HHH decides to 
>>>>>>>>>>>>>>>>> abort and return, then the DDD that it is emulating 
>>>>>>>>>>>>>>>>> WILL return, just after HHH has stopped its emulation.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You just confuse the behavior of DDD with the PARTIAL 
>>>>>>>>>>>>>>>>> emulation that HHH does, because you lie about your 
>>>>>>>>>>>>>>>>> false "tautology".
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Denying a tautology seems to make you a liar. I only
>>>>>>>>>>>>>>>>>> say "seems to" because I know that I am fallible.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Claiming a false statement is a tautology only make you 
>>>>>>>>>>>>>>>>> a liar.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> In this case, you lie is that the HHH that you are 
>>>>>>>>>>>>>>>>> talking about do the "correct emulation" you base you 
>>>>>>>>>>>>>>>>> claim on.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> That is just a deception like the devil uses, has just 
>>>>>>>>>>>>>>>>> a hint of truth, but the core is a lie.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> What I say is provably correct on the basis of the
>>>>>>>>>>>>>>>> semantics of the x86 language.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Nope.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The x86 language says DDD will Halt if HHH(DDD) returns a 
>>>>>>>>>>>>>>> value.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> HHH is called by main() there is no directly executed DDD()
>>>>>>>>>>>>>> any where in the whole computation.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Except in your requirements, and we can see what it does by 
>>>>>>>>>>>>> adding a call to DDD from main, since nothing in your 
>>>>>>>>>>>>> system calls main.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> All that you need to know is that there is not any
>>>>>>>>>>>> directly executed DDD() anywhere in the computation.
>>>>>>>>>>>
>>>>>>>>>>> But there ccould be, and the behavior of it is what matters.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The key error of the halting problem proofs all of these
>>>>>>>>>> years has been the false assumption that a halt decider
>>>>>>>>>> must report on the behavior of the computation that itself
>>>>>>>>>> is contained within.
>>>>>>>>>
>>>>>>>>> But it isn't a false assemption, but an actual requirement.
>>>>>>>>>
>>>>>>>>> A Halt Decider must be able to correctly answer for ANY Turing 
>>>>>>>>> Machine represented as its input.
>>>>>>>>>
>>>>>>>>> ANY includes those that are built from a copy of itself.
>>>>>>>>>
>>>>>>>>> So, a Halt Decider needs to be able to correctly answer about 
>>>>>>>>> programs that include copies of itself, even with contrary 
>>>>>>>>> behavior, which is what makes it impossible to compute.
>>>>>>>>>
>>>>>>>>> You seem to confuse non-computable with invalid, it seems in 
>>>>>>>>> part because you don't understand the difference between 
>>>>>>>>> knowledge and truth.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Everyone has simply assumed that the behavior of the
>>>>>>>>>> input to a decider must exactly match the direct execution
>>>>>>>>>> of this input. They only did this because everyone rejected
>>>>>>>>>> simulation out-of-hand without review.
>>>>>>>>>
>>>>>>>>> Because that is the DEFINITION of what it is to decide on.
>>>>>>>>>
>>>>>>>>> You just don't understand what a requirement is.
>>>>>>>>>
>>>>>>>>> Since the DEFINITION of "Correct Simulation" that you are 
>>>>>>>>> trying to use (from a UTM) means a machine the EXACTLY 
>>>>>>>>> reproduces the behavior of the direct exectution of the machine 
>>>>>>>>> described by the input, the correct simulation must exactly 
>>>>>>>>> match the behavior of the direct execution.
>>>>>>>>>
>>>>>>>>> You can't get out of it by trying to lie about it being different.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> This caused them to never notice that the input simulated
>>>>>>>>>> according to its correct semantics does call its own decider
>>>>>>>>>> in recursive simulation thus cannot possibly return to its
>>>>>>>>>> caller. The Linz proof is sufficiently isomorphic so this equally
>>>>>>>>>> applies to the Linz TM proof.
>>>>>>>>>
>>>>>>>>> Nope, just shows you don't know what "Correct" means.
>>>>>>>>>
>>>>>>>>> Your proof is NOT "sufficiently isomorphic" since by your own 
>>>>>>>>> claims it is clearly not even Turing Complete, so no where near 
>>>>>>>>> isomorphic.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> If HHH were to report on the direct execution of DDD it would
>>>>>>>>>> be breaking the definition of a halt decider that only computes
>>>>>>>>>> the mapping from its input...
>>>>>>>>>
>>>>>>>>> Nope. Since the mapping that it is supposed to compute is 
>>>>>>>>> DEFINED as based on the direct exectut
>>>>>>>>>
>>>>>>>>
>>>>>>>> No it never has been this. I has always been a mapping
>>>>>>>> from the behavior that the finite string specifies. It
>>>>>>>> has never been the behavior of the actual computation
>>>>>>>> that the decider is contained within.
>>>>>>>
>>>>>>>
>>>>>>> And thatg behavior is specified to be the behavior of the program 
>>>>>>> the input represents. PERIOD.
>>>>>>>
>>>>>>
>>>>>> That has never been true. It is always the case that every
>>>>>> decider of any kind only computes the mapping from its input
>>>>>> finite string and never gives a rat's ass about anything else
>>>>>> anywhere else.
>>>>>
>>>>> No, you are confusing capability with requirements.
>>>>>
>>>>> A "Foo Decider" has ALWAYS been required to compute the "Foo" 
>>>>> mapping, as that mapping is defined.
>>>>>
>>>>> The "Halting" mapping is defined as the behavior of the machine/ 
>>>>> input represented by the input, so the input needs to be a 
>>>>> representation of the program and input and the decider tries to 
>>>>> compute the mapping of that representation to the behavior that 
>>>>> program represents.
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