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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: D(D) simulated by H cannot possibly reach past its own line 03
Date: Fri, 3 May 2024 23:24:47 -0400
Organization: i2pn2 (i2pn.org)
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On 5/3/24 8:13 PM, olcott wrote:
> On 5/3/2024 8:40 AM, olcott wrote:
>> 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 void main()
>> 10 {
>> 11   H(D,D);
>> 12 }
>>
>> We are examining the behavior of D(D) for every possible H/D pair
>> where 1 to N steps of D(D) are simulated by H.
>>
>> *Execution Trace*
>> Line 11: main() invokes H(D,D) that simulates D(D)
>>
>> *keeps repeating* (unless aborted)
>> Line 01
>> Line 02
>> 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.
>>
>> (a) It is a verified fact that for every possible H/D pair where
>> 1 to N steps of D(D) are simulated by H that this simulated D(D)
>> cannot possibly reach past its own line 03.
>>
> 
> I only had to add this new step because I found that some people just
> do not understand that when the executed H(D,D) aborts its simulated
> input that all of the nested simulations (if any) immediately totally 
> stop running. No simulated H ever returns any value to any simulated D.
> We can sum this up much more concisely with (a).

Fixing definitions is good.

The refutation of (a) that I gave didn't use that "loop hole" and both 
of the examples actually simulated the steps to past line 3.

After all, how can you simulate past line 3 and not simulate any steps?

The no-simulation case was just showing that using your conclusion from 
(a) and saying that H is correct to abort here, allows, with just as 
valid of logic, to allow a decider to trivally decide to abort either 
after 0, or with your modification, after 1 step, to just abort and say 
it couldn't reach the end.

> 
>> (b) Rebuttals must show a counter example where 1 to N steps
>> of D(D) are simulated by H and the simulated D(D) reaches past
>> its own line 03.

Was done.

You need to refute that example or you are just admitting you are a liar 
that makes claims that have been disproven.

The fact that you don't understand how it was disproven, the fact that 
you know that the statements were made and you haven't refuted it, means 
your claims have become unproven statements, and thus not valid to claim.

>>
>> *Termination Analyzer H is Not Fooled by Pathological Input D*
>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
>>
>> *Fully operational code implemented in the x86utm operating system*
>> https://github.com/plolcott/x86utm
>>
>>
>>
>