Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott 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: References: 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: 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