Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 10:51:40 -0500
Organization: A noiseless patient Spider
Lines: 39
Message-ID: <vvamqc$o6v5$4@dont-email.me>
References: <GE4SP.47558$VBab.42930@fx08.ams4>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Mon, 05 May 2025 17:51:41 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="0a6320ec149f030cd98ca15e4d2d5e5f";
	logging-data="793573"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18Xn0j5pQ5p34Kv6BvcHdIU"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:C6wbWvGWLn5SMKpJXPcEFaZwYgY=
X-Antivirus: Norton (VPS 250505-2, 5/5/2025), Outbound message
Content-Language: en-US
In-Reply-To: <GE4SP.47558$VBab.42930@fx08.ams4>
X-Antivirus-Status: Clean

On 5/5/2025 10:17 AM, Mr Flibble wrote:
> What constitutes halting problem pathological input:
> 
> Input that would cause infinite recursion when using a decider of the
> simulating kind.
> 
> Such input forms a category error which results in the halting problem
> being ill-formed as currently defined.
> 
> /Flibble

I prefer to look at it as a counter-example that refutes
all of the halting problem proofs.

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

https://github.com/plolcott/x86utm

The x86utm operating system includes fully
operational HHH and DD.
https://github.com/plolcott/x86utm/blob/master/Halt7.c

When HHH computes the mapping from *its input* to
the behavior of DD emulated by HHH this includes
HHH emulating itself emulating DD. This matches
the infinite recursion behavior pattern.

Thus the Halting Problem's "impossible" input
is correctly determined to be non-halting.

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