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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Simulating termination analyzers by dummies --- What does halting
 mean?
Date: Tue, 18 Jun 2024 12:25:44 -0500
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On 6/18/2024 12:06 PM, joes wrote:

void DDD()
{
   H0(DDD);
}

DDD correctly simulated by any H0 cannot possibly halt.

> DDD halts iff H0 halts.

Halting is a technical term-of-the-art that corresponds
to terminates normally. Because Turing machines are
abstract mathematical objects there has been no notion
of abnormal termination for a Turing machine.

We can derive a notion of abnormal termination for Turing
machines from the standard terms-of-the-art.

Some TM's loop and thus never stop running, this is classical
non-halting behavior. UTM's simulate Turing machine descriptions.
This is the same thing as an interpreter interpreting the
source-code of a program.

A UTM can be adapted so that it only simulates a fixed number
of iterations of an input that loops. When this UTM stops
simulating this Turing machine description we cannot correctly
say that this looping input halted.

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