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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 14:46:44 -0500
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On 3/29/2025 2:25 PM, dbush wrote:
> On 3/29/2025 3:19 PM, olcott wrote:
>> On 3/29/2025 2:01 PM, dbush wrote:
>>> On 3/29/2025 2:58 PM, olcott wrote:
>>>> On 3/29/2025 1:37 PM, dbush wrote:
>>>>> On 3/29/2025 2:15 PM, olcott wrote:
>>>>>> On 3/29/2025 4:31 AM, joes wrote:
>>>>>>> Am Fri, 28 Mar 2025 14:27:36 -0500 schrieb olcott:
>>>>>>>> On 3/28/2025 2:17 PM, dbush wrote:
>>>>>>>>> On 3/28/2025 3:02 PM, olcott wrote:
>>>>>>>>>> On 3/28/2025 1:12 PM, dbush wrote:
>>>>>>>>>>> On 3/28/2025 1:57 PM, olcott wrote:
>>>>>>>>>>>> On 3/27/2025 9:33 PM, dbush wrote:
>>>>>>>>>>>>> On 3/27/2025 10:10 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/27/2025 8:24 PM, dbush wrote:
>>>>>>>>>>>>>>> On 3/27/2025 9:21 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/27/2025 8:09 PM, dbush wrote:
>>>>>>>>>>>>>>>>> On 3/27/2025 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/27/2025 7:38 PM, dbush wrote:
>>>>>>>
>>>>>>>>>>>>>>> Good, because that's all that's required for a solution 
>>>>>>>>>>>>>>> to the
>>>>>>>>>>>>>>> halting problem:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There are sometimes when the behavior of TM Description D
>>>>>>>>>>>>>> correctly simulated by UTM1 does not match the behavior 
>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>> simulated by UTM2.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Irrelevant, because to satisfy the requirements, the 
>>>>>>>>>>>>> behavior of
>>>>>>>>>>>>> the described machine when executed directly must be reported.
>>>>>>>>>>>>
>>>>>>>>>>>> I HAVE PROVED THAT THE REQUIREMENT IS WRONG NITWIT.
>>>>>>> According to what? WE require it. YOU are answering a different 
>>>>>>> question.
>>>>>>>
>>>>>>>>>>> Category error.
>>>>>>>>>>> I want to know if any arbitrary algorithm X with input Y will 
>>>>>>>>>>> halt
>>>>>>>>>>> when executed directly.
>>>>>>>>>>
>>>>>>>>>> It is 100% impossible for any TM to take another executing TM 
>>>>>>>>>> as its
>>>>>>>>>> input.
>>>>>>> Quit that.
>>>>>>>
>>>>>>>>> But it can take a complete description of a TM that
>>>>>>>>
>>>>>>>> Is not always a perfect proxy for the behavior of the direct 
>>>>>>>> execution
>>>>>>>> of the underlying machine.
>>>>>>
>>>>>>> Uh yes it is.
>>>>>>>
>>>>>>
>>>>>> That my proof that I am correct
>>>>>> is over your head is less than
>>>>>> no rebuttal what-so-ever.
>>>>>
>>>>> The fact that such TM description can be given to a UTM which will 
>>>>> exactly replicate the behavior of the described TM when executed 
>>>>> directly proves otherwise is apparently over your head.
>>>>>
>>>>
>>>> One cannot correctly ignore the effect that a specified
>>>> pathological relationship has between its simulator
>>>> and its input on the behavior of this input.
>>>>
>>>
>>> All it means is that HHH does not correctly map DDD to 1 as per the 
>>> requirements:
>>>
>>
>> int sum(int x, int y) { return x + y; }
>> In the same way that sum(2,3) cannot be mapped to 7.
> 
> It can, it just wouldn't meet the requirements of the mathematical "sum" 
> function.
> 

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

Likewise if HHH reported on the behavior of the
directly executed DD it would not be reporting
on the behavior that its actual input specifies.

>>
>> Computations apply a set of finite string transformation
>> rules to an input finite string to derive an output finite
>> string.
> 
> And if the mapping in question is not computable, no computation can do it.
> 

The same way that the sum(2,3) cannot report 7.
If it is required to report 7 then the requirement is wrong.

>>
>> The semantic property that input DDD specifies to HHH
>> is non-halting.
>>
> 
> int greater_than_5(int x)
> {
>      return 1;
> }
> 
> Similarly, the semantic property that input 3 specifies to 
> greater_than_5 is a number greater than 5.

The name of a function is not binding on its algorithm.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer