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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: D(D) simulated by H cannot possibly reach past its own line 03
Date: Sun, 2 Jun 2024 11:50:30 +0200
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Op 03.mei.2024 om 15:40 schreef olcott:
> 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.

The Linz proof is based on the pathological relation ship that D 
contradicts the result of H. This is expressed in lines 04, 05, 06 of D, 
above.
It is strange that olcott claims that the simulation never sees the 
pathological part of D. He now seems to shift the meaning of 
pathological to the mere fact that D calls H. Lines 04, 05, and 06 are 
completely irrelevant.
In fact, any function that calls H now become pathological.

E.G. if we replace D with a function P that only returns its own 
Halt_Status:

01 int P(ptr x)
02 {
03   int Halt_Status = H(x, x);
04
05
06   return Halt_Status;
07 }

Then we would normally expect that, because H is required to halt, P 
would halt as well. But the simulation of P by H does not halt. So, P, 
when it halts, reports that it not halting.

The problem here is, that H is unable to simulate itself to its final 
state. That has no relation with the Linz proof, it is a problem of H.

So, there is another *Simulation invariant*
H correctly simulated by H cannot possibly reach its own return.

> 
> (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.

(aa) If so, then it is also a verified fact that for every possible H/D 
pair where1 to N steps of H are simulated by H that the simulated H 
cannot possibly reach to its own return.

> 
> (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.

(bb) Rebuttals must show the trace where 1 to N steps of H are simulated 
by H and the simulated H reaches its return.