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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Simplified proof that DDD correctly simulated by HHH does not
 halt
Date: Sun, 9 Jun 2024 11:07:19 -0500
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On 6/9/2024 9:19 AM, olcott wrote:

*You must know the C programming language to understand this*

typedef void (*ptr)(); // pointer to void function

01   void HHH(ptr P, ptr I)
02   {
03     P(I);
04     return;
05   }
06
07   void DDD(int (*x)())
08   {
09     HHH(x, x);
10     return;
11   }
12
13   int main()
14   {
15     HHH(DDD,DDD);
16   }
17

*The truth preserving transformations are anchored in the*
*semantics of the C programming language that specifies*
line 15 of main executes HHH(DDD,DDD);
line 03 of HHH  executes DDD(DDD)
line 09 of DDD  executes HHH(DDD,DDD);

This can be summed up as simply comprehending
infinite recursion <is> the proof that

In the above Neither DDD nor HHH ever reach their
own return statement thus never halt.

It is the exact same process that HH(DD,DD) recognizes
this exact same infinite recursion behavior pattern.

Most of my reviewers incorrectly believe that when HH(DD,DD)
aborts its simulated input that this simulated input halts.
That is not the case. In the theory of computation "halting"
essentially means "terminated normally" in software engineering.

When HHH is a simulating halt decider just like HH then
DDD correctly simulated by HHH cannot possibly terminate normally

> 
> When HHH is a simulating halt decider then HHH sees that
> DDD correctly simulated by HHH cannot possibly reach its
> own return statement, AKA
> 
>     simulating halt decider HHH correctly simulates its input DDD
>     until HHH correctly determines that its simulated DDD would never
>     stop running unless aborted
> 
> *as defined here*
> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>    If simulating halt decider H correctly simulates its input D
>    until H correctly determines that its simulated D would never
>    stop running unless aborted then
> 
>    H can abort its simulation of D and correctly report that D
>    specifies a non-halting sequence of configurations.
> </MIT Professor Sipser agreed to ONLY these verbatim words10/13/2022>
> 
> 

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