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Path: ...!eternal-september.org!feeder3.eternal-september.org!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: Tue, 6 May 2025 10:36:00 -0500 Organization: A noiseless patient Spider Lines: 56 Message-ID: <vvda90$37t3c$2@dont-email.me> References: <GE4SP.47558$VBab.42930@fx08.ams4> <vvamqc$o6v5$4@dont-email.me> <vvan7q$o4v0$1@dont-email.me> <ts5SP.113145$_Npd.41800@fx01.ams4> <vvat0g$vtiu$1@dont-email.me> <vvatf3$o4v0$3@dont-email.me> <vvaut0$vtiu$4@dont-email.me> <vvav6o$o4v0$4@dont-email.me> <vvb329$15u5b$1@dont-email.me> <vvb37g$1451r$1@dont-email.me> <vvb43f$15u5b$4@dont-email.me> <vvb4ok$o4v0$9@dont-email.me> <vvb52g$15u5b$6@dont-email.me> <vvclr6$2lui8$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 06 May 2025 17:36:01 +0200 (CEST) Injection-Info: dont-email.me; posting-host="4d3877b25e07ae675aebb853b858fd37"; logging-data="3404908"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/2m1PP3Up+BJC/y7rgaOyL" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:c7XTFRR6/GZEAEGGk7yBjT35Wgw= X-Antivirus: Norton (VPS 250506-2, 5/6/2025), Outbound message Content-Language: en-US X-Antivirus-Status: Clean In-Reply-To: <vvclr6$2lui8$1@dont-email.me> Bytes: 3537 On 5/6/2025 4:47 AM, Mikko wrote: > On 2025-05-05 19:54:55 +0000, olcott said: > >> On 5/5/2025 2:49 PM, dbush wrote: >>> On 5/5/2025 3:38 PM, olcott wrote: >>>> On 5/5/2025 2:23 PM, Richard Heathfield wrote: >>>>> On 05/05/2025 20:20, olcott wrote: >>>>>> Is "halts" the correct answer for H to return? NO >>>>>> Is "does not halt" the correct answer for H to return? NO >>>>>> Both Boolean return values are the wrong answer >>>>> >>>>> Or to put it another way, the answer is undecidable, QED. >>>>> >>>>> See? You got there in the end. >>>>> >>>> >>>> Is this sentence true or false: "What time is it?" >>>> is also "undecidable" because it is not a proposition >>>> having a truth value. >>>> >>>> Is this sentence true or false: "This sentence is untrue." >>>> is also "undecidable" because it is not a semantically sound >>>> proposition having a truth value. >>>> >>>> Can Carol correctly answer “no” to this (yes/no) question? >>>> >>>> Both Yes and No are the wrong answer proving that >>>> the question is incorrect when the context of who >>>> is asked is understood to be a linguistically required >>>> aspect of the full meaning of the question. >>> >>> And "does algorthm X with input Y halt when executed directly" has a >>> single well defined answer. >>> >> >> That is not even the actual question. >> >> Does the finite string input DD to HHH specify >> a computation that halts? No it does not. > > That question is a category error. The halting question is not about > finite strings but about computations. > HHH must compute the mapping from its finite string of x86 code input to the actual behavior that this finite string input specifies. The same thing goes for TM's H must compute the mapping from the finite string TM source-code input to the behavior that this TM source-code specifies. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer