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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by pure function H cannot possibly reach
 its, own line 06 ---
Date: Sun, 26 May 2024 13:48:41 -0400
Organization: i2pn2 (i2pn.org)
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On 5/26/24 1:26 PM, olcott wrote:
> On 5/26/2024 12:16 PM, Richard Damon wrote:
>> On 5/26/24 1:01 PM, olcott wrote:
>>> On 5/26/2024 11:31 AM, Richard Damon wrote:
>>>> On 5/26/24 10:13 AM, olcott wrote:
>>>>> On 5/26/2024 6:43 AM, Richard Damon wrote:
>>>>>
>>>>> typedef int (*ptr)();  // ptr is pointer to int function in C
>>>>> 00       int H(ptr p, ptr i);
>>>>> 01       int D(ptr p)
>>>>> 02       {
>>>>> 03         int Halt_Status = H(p, p);
>>>>> 04         if (Halt_Status)
>>>>> 05           HERE: goto HERE;
>>>>> 06         return Halt_Status;
>>>>> 07       }
>>>>> 08
>>>>> 09       int main()
>>>>> 10       {
>>>>> 11         H(D,D);
>>>>> 12         return 0;
>>>>> 13       }
>>>>>
>>>>>
>>>>>> Because, as I have said, the answer and reasoning changes 
>>>>>> depending on what you acknowledged are the implications of your 
>>>>>> stipulations. For instance, if your actual understanding of being 
>>>>>> a "Pure Function" is that the program is the equivalent of a 
>>>>>> Turing Machine, then we need to add a strictness to the definition 
>>>>>> that isn't normally used for just "Pure Functions", like accessing 
>>>>>> value of registers like the program counter or stack pointer might 
>>>>>> not be allowed in some cases. (which breaks you H).
>>>>>>
>>>>>
>>>>> Since we can see (and you already agreed) that D correctly simulated
>>>>> by pure simulator H remains stuck in infinite recursive simulation 
>>>>> then
>>>>> we also know that D never reaches its own line 06 and halts in less
>>>>> than an infinite number of correctly simulated steps.
>>>>
>>>> But it depends on what H actually does, which you refuse to agree to.
>>>>
>>>
>>> When I specify that D is correctly simulated by pure function H, that
>>> means that H is a pure simulator that stops simulating D after some
>>> finite number of correctly simulated steps. There is absolutely nothing
>>> else that needs to be known about H besides this.
>>>
>>
>> And, do you accept that this exact description means that H is NOT the 
>> computational equivalent of a Turing Machine, and that this simulation 
>> doesn't prove that its input is not a non-halting program?
>>
> 
> In other words you are saying that it is 100% totally impossible to
> adapt an actual UTM so that it stops simulating after a finite number of
> steps.

Yep, at least and have it still be a UTM.

IMPOSSIBLE BY DEFINITION.

That is like talking about a circle that is a square.

You just proved why I am requiring you to accept the implications since 
you clearly don't know what some of the words you use mean.

> 
> When we see that D correctly simulated by pure simulator H would remain
> stuck in recursive simulation then we also know that D never reaches its
> own line 06 and halts in less than an infinite number of correctly
> simulated steps.

Nope, not if H has aborted its simulation.

You might be describing the behavior of one particular input D given to 
one particular analyzer H that doesn't ever stop its simulation, but 
that isn't the H that you are actually talking about, just the one that 
you are trying to LIE about being the "same".

> 
> This means that D correctly simulated by pure function H also never
> reaches it own line 06 and halts.

Nope, not if H has aborted its simulation. If H aborts its simulation 
and returns 0, the D will actually reach its own line 6 and halt. That 
IS the behavior specified by your D.

H's simulation won't see that, but that is why H got the wrong answer.

So, you need to be clear what you words mean, which you aren't.

> 
>> Failure to acknowledge this means that you don't understand the 
>> meaning of the terms you used, and that you accept the implications.
> 
> I am not the one saying that it is 100% impossible to adapt an ordinary
> UTM so that it stops simulating after a finite number of steps.
> 

Which is why you are wrong.

That is like talking about the 4 sides of a circle (because you think a 
square can be a circle).

Yes, you can take the design of a UTM, and change it so that it is no 
longer a UTM, but a partial simulator that halts after a finite number 
of steps. It just isn't a UTM any more.

Like talking an Electric car and removing that battery and electric 
motor and "improving" it with a gas engine. You may still have a car, 
but it is no longer an "Electric Vehicle".