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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sun, 30 Mar 2025 16:06:33 +0200
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Op 29.mrt.2025 om 22:07 schreef olcott:
> On 3/29/2025 3:45 PM, Fred. Zwarts wrote:
>> Op 29.mrt.2025 om 20:03 schreef olcott:
>>> On 3/29/2025 10:23 AM, dbush wrote:
>>>> On 3/29/2025 11:12 AM, olcott wrote:
>>>>> On 3/28/2025 11:00 PM, dbush wrote:
>>>>>> On 3/28/2025 11:45 PM, olcott wrote:
>>>>>>>
>>>>>>> It defines that it must compute the mapping from
>>>>>>> the direct execution of a Turing Machine
>>>>>>
>>>>>> Which does not require tracing an actual running TM, only mapping 
>>>>>> properties of the TM described. 
>>>>>
>>>>> The key fact that you continue to dishonestly ignore
>>>>> is the concrete counter-example that I provided that
>>>>> conclusively proves that the finite string of machine
>>>>> code input is not always a valid proxy for the behavior
>>>>> of the underlying virtual machine.
>>>>
>>>> In other words, you deny the concept of a UTM, which can take a 
>>>> description of any Turing machine and exactly reproduce the behavior 
>>>> of the direct execution.
>>>
>>> I deny that a pathological relationship between a UTM and
>>> its input can be correctly ignored.
>>>
>>> When this pathological relationship changes this behavior
>>> we cannot simply pretend that the behavior is not changed.
>>>
>>>
>>
>> When solving a problem, it is stupid to choose a tool that has a 
>> pathological relation with the problem. 
> 
> A termination analyzer cannot reject itself, yet it can
> reject an input. This input was intentionally defined
> to try to fool this termination analyzer.
> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> On the other hand when this same input DD is simulated
> by the termination analyzer that DD defined a pathological
> relationship to IT DOES SPECIFY NON-TERMINATING BEHAVIOR.
> 

We can ask whether we can create a hammer that can hit all possible 
nails on the head. It can be proven that no such hammer exists, because 
we can always attach a nail to the hammer upside down, so that the 
hammer cannot hit it on its head.
Olcott would call that a 'pathological relationship' between hammer and 
nail. I think he would argue that for such a pathological relationship 
between hammer and nail we need another definition of 'hitting 
behaviour', because the original requirement ignores the pathological 
relationship. So, when we define a 'hitting behaviour' as when the 
hammer is halfway down in an attempt to reach the nail, we see that he 
can construct a hammer and say that it correctly shows 'hitting 
behaviour' to the nail when it is halfway down, because the requirement 
to hit it on the head is logically impossible. :-)