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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Mon, 27 May 2024 08:52:09 -0500
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On 5/27/2024 3:11 AM, Mikko wrote:
> On 2024-05-26 16:50:21 +0000, olcott said:
> 

<snip>
So that: *Usenet Article Lookup*
http://al.howardknight.net/
can see the whole message now that
*the Thai spammer killed Google Groups*

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       }

>> 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.
> 
> Which means that H never terminates. You said that by your definition
> a function that never terminates is not a pure function. Therefore
> H, if it exists, is not a pure function, and the phrase "pure function
> H" does not denote.
> 

*I should have said that more clearly*
*That is why I need reviewers*
*Here it is more clearly*

When we hypothesize that H is a pure simulator we see that D correctly
simulated by pure simulator H remains stuck in recursive simulation thus
never reaches its own simulated final state at its line 06 and halts. In
this case H does not halt, thus is neither a pure function nor a
decider.

 From this we correctly conclude that D correctly simulated by pure
function H never reaches its simulated final state at its own line 06
and halts in Less than an infinite (AKA finite) number of simulated
steps. Here is a concrete example of that:

https://en.wikipedia.org/wiki/Googolplex
When pure function H correctly simulates a Googolplex ^ Googolplex
number of steps of D, then D never reaches its simulated final state
at its own line 06 and halts. Pure function H halts after this finite
number of steps of correct simulation.

In other words when the *INPUT* to H(D,D) is correctly simulated by
either pure simulator H or pure function H this correctly simulated
*INPUT* never halts no matter what, thus the INPUT to H(D,D) is
definitely non halting.

*This is STEP ONE of my four step proof*
STEP TWO applies these same ideas to the Peter Linz HP proof.
STEP THREE shows how the Linz Ĥ.H sees the behavior of its recursive
      simulations.
STEP FOUR shows why the behavior of the INPUT is the correct basis.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer