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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H
Date: Tue, 7 May 2024 07:18:42 -0400
Organization: i2pn2 (i2pn.org)
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On 5/7/24 3:30 AM, Mikko wrote:
> On 2024-05-06 18:28:37 +0000, olcott said:
> 
>> On 5/6/2024 11:19 AM, Mikko wrote:
>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>
>>>> The x86utm operating system: https://github.com/plolcott/x86utm enables
>>>> one C function to execute another C function in debug step mode.
>>>> Simulating Termination analyzer H simulates the x86 machine code of its
>>>> input (using libx86emu) in debug step mode until it correctly matches a
>>>> correct non-halting behavior pattern proving that its input will never
>>>> stop running unless aborted.
>>>>
>>>> Can D correctly simulated by H terminate normally?
>>>> 00 int H(ptr x, ptr x)  // ptr is pointer to int function
>>>> 01 int D(ptr x)
>>>> 02 {
>>>> 03   int Halt_Status = H(x, x);
>>>> 04   if (Halt_Status)
>>>> 05     HERE: goto HERE;
>>>> 06   return Halt_Status;
>>>> 07 }
>>>> 08
>>>> 09 int main()
>>>> 10 {
>>>> 11   H(D,D);
>>>> 12 }
>>>>
>>>> *Execution Trace*
>>>> Line 11: main() invokes H(D,D);
>>>>
>>>> *keeps repeating* (unless aborted)
>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>>
>>>> *Simulation invariant*
>>>> D correctly simulated by H cannot possibly reach past its own line 03.
>>>>
>>>> The above execution trace proves that (for every H/D pair of the
>>>> infinite set of H/D pairs) each D(D) simulated by the H that this D(D)
>>>> calls cannot possibly reach past its own line 03.
>>>
>>> When you say "every H/D pair" you should specify which set of pairs
>>> you are talking about. As you don't, your words don't mean anything.
>>>
>>
>> Every H/D pair in the universe where D(D) is simulated by the
>> same H(D,D) that D(D) calls. This involves 1 to ∞ steps of D
>> and also includes zero to ∞ recursive simulations where H
>> H simulates itself simulating D(D).
> 
> "In the universe" is not a set. In typical set theories like ZFC there
> is no universal set.


No, it shows that he is just thinking of Nieve set theory, you know, the 
one that was proven broken.

> 
> Usually the best way to introduce a set of pairs is that first two
> sets are specified and then a rule that selects some pairs from
> the Cartesian product of those two sets.
> 
> In the current case the first set could be the set programs that
> take two input values (possibly of some specific type) and returns
> a Boolean value, and the second set could be programs that take
> one input value (of the same type as the programs in the first set).
> Or whatever best serves your purposes.
>