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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: What is the correct halt status for HHH(DDD) ?
Date: Sat, 13 Jul 2024 13:25:20 -0400
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On 7/13/24 12:48 PM, olcott wrote:
> What is the correct halt status for an input to
> a simulating termination analyzer that calls its
> own termination analyzer?
> 
> typedef void (*ptr)();
> int HHH(ptr P);
> 
> void DDD()
> {
>    HHH(DDD);
> }
> 
> int main()
> {
>    HHH(DDD);
> }
> 

Halting.

Since HHH defined to be a termination analyzer, by that definition it 
must return to its caller.

Since DDD has no inputs, its behavior isn't affected by any inputs, and 
thus DDD will halt for ALL input conditions, so for HHH to be a correct 
termination analysizer it needs to return the value to indicate Halting.

Your version can't do that, so either fails to be a proper decider, or 
gets the wrong answer.

The Flibble version could get this correct, if the structure allows it 
to properly detect that DDD is actually calling HHH, which puts us 
outside of the Turing Equivalency rules, but can be done in that C code.