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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Mon, 27 May 2024 10:10:54 -0400
Organization: i2pn2 (i2pn.org)
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On 5/27/24 9:52 AM, olcott wrote:
> 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.

But when you hypothesize that H is actually a "pure simulator" 
(presumably one that never aborts) then you are creating a D that uses 
that pure simulator, and are ONLY deriving conclusions for such a D.

The results do NOT apply for a D built on a different H, that happens to 
abort its simulation,

> 
>  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:

Right, but ONLY for a D built on such a pure simulator. It says nothing 
if you build a

> 
> 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.

But then H is NOT that "Pure Simulator" you were imagining above, and 
thus you can't use that result.

> 
> 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.

Nope. You might be able to claim that your H can't reach the final step 
in its simulation, but you can't claim that the input doesn't halt when 
simulated by a Pure Simulator. You have admited that if H(D,D) returns 0 
then D(D) will halt.

You then try to claim, without being able to prove the false statement, 
that somehow it is ok for H to give the wrong answer, but of course that 
is just an admission that you logic system is broken and inconsistent.


> 
> *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.
> 

And it seems ALL You steps have similar error, because you just don't 
understand what you are talking about. This is the problem of trying to 
work in a system you haven't actually studied.