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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: Sun, 11 Aug 2024 13:06:22 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <86c21e8a63450bf8b0c32f4f17ba0b503a914fe0@i2pn2.org>
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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 
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