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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD correctly emulated by HHH --- Totally ignoring invalid
 rebuttals ---PSR---
Date: Sat, 8 Mar 2025 22:35:39 -0500
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On 3/8/2025 9:36 PM, dbush wrote:
> On 3/8/2025 9:30 PM, olcott wrote:
>> On 3/8/2025 7:43 PM, dbush wrote:
>>> On 3/8/2025 8:24 PM, olcott wrote:
>>>> On 3/8/2025 6:56 PM, dbush wrote:
>>>>> On 3/8/2025 7:29 PM, olcott wrote:
>>>>>> On 3/8/2025 5:31 PM, dbush wrote:
>>>>>>> On 3/8/2025 6:23 PM, olcott wrote:
>>>>>>>> On 3/8/2025 4:58 PM, dbush wrote:
>>>>>>>>> On 3/8/2025 5:42 PM, olcott wrote:
>>>>>>>>>> On 3/8/2025 9:00 AM, dbush wrote:
>>>>>>>>>>> On 3/8/2025 9:03 AM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> Apparently you don't understand that inputs to a
>>>>>>>>>>>> simulating termination analyzer specifying infinite
>>>>>>>>>>>> recursion or recursive emulation cannot possibly
>>>>>>>>>>>> reach their own final state and terminate normally.
>>>>>>>>>>>
>>>>>>>>>>> Apparently you don't understand that inputs to a termination 
>>>>>>>>>>> analyzer, simulating or otherwise, are specified by the 
>>>>>>>>>>> specification that is the halting function:
>>>>>>>>>>>
>>>>>>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed 
>>>>>>>>>>> directly
>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when 
>>>>>>>>>>> executed
>>>>>>>>>>>
>>>>>>>>>>> And HHH(DD)==0 fails to meet the above specification
>>>>>>>>>>
>>>>>>>>>> *THIS IS A SEMANTIC TAUTOLOGY THUS IMPOSSIBLY FALSE*
>>>>>>>>>> Replacing the code of HHH with an unconditional simulator and 
>>>>>>>>>> subsequently running HHH(DD) cannot possibly reach
>>>>>>>>>> its own "ret" instruction and terminate normally
>>>>>>>>>> because DD calls HHH(DD) in recursive emulation.
>>>>>>>>>>
>>>>>>>>>> It is ridiculously stupid to believe that HHH must
>>>>>>>>>> report on behavior other than the above behavior.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> It must if it is to be classified as a halt decider or 
>>>>>>>>> termination analyzer as per the definition.
>>>>>>>>
>>>>>>>> In other words you believe that HHH 
>>>>>>>
>>>>>>> Is required to map the halting function to meet the requirements 
>>>>>>> to be a halt decider / termination analyzer.
>>>>>>>
>>>>>>
>>>>>> HHH must map from the input finite string DD
>>>>>> to the behavior that this finite string specifies
>>>>>
>>>>> And what it specifies, to be considered a solution to the halting 
>>>>> problem, is given by the specification:
>>>>>
>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>> instructions) X described as <X> with input Y:
>>>>>
>>>>> A solution to the halting problem is an algorithm H that computes 
>>>>> the following mapping:
>>>>>
>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
>>>>>
>>>>
>>>> In the same way that Sum(5,3) == 9
>>>> That is misconception is very widely held
>>>> does not make it not a misconception.
>>>>
>>>
>>> In other words, you have no rebuttal to the fact that HHH doesn't 
>>> meet the requirements to be a solution to the halting problem.
>>
>> If the halting problem actually requires that the "decider"
>> report on behavior other than what the input specifies
>> then its notion of a halting decider is not even a decider
>> in computer science.
>>
> 
> The halting problem requires that the halting function is mapped:
> 
> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
> 
> So by this specification, (<X>,Y) specifies the behavior of X(Y) when 
> executed directly.
> 
> Any algorithm that does not compute this mapping is not a solution to 
> the halting problem.

Your copy-paste answer to multiple threads indicates you have no real 
rebuttal for what others have said.

Unless you respond to this thread, I'll take your lack of response to 
mean that you accept that the above specification is required to be a 
solution to the halting problem.