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From: Richard Damon <richard@damon-family.org>
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 22:21:37 -0400
Organization: i2pn2 (i2pn.org)
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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.

Now, it is only CAPABLE of computing a computable mapping, like a finite 
length emulation of the input, and since it has been shown that Halting 
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