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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 15:25:46 -0400
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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.

> 
> 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 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.