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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: Sat, 10 Aug 2024 21:38:23 -0500
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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.
> 
> How that isn't the "mapping" of the input to a Halt Decider seems to put 
> a big hole in your argument.
> 
> So, the behavior of the program the input describes *IS* the mapping 
> that HHH needs to try to compute to be a halt decider, as that is the 
> mapping that Halting defines.
> 
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