Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!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: Tue, 6 May 2025 21:40:14 -0500 Organization: A noiseless patient Spider Lines: 124 Message-ID: References: <5b84f927f8052f5392b625cef9642140d439d1c7@i2pn2.org> <1a99b2ee77f8c0d1ff37e5febb47c5be17b2d4fb@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 07 May 2025 04:40:15 +0200 (CEST) Injection-Info: dont-email.me; posting-host="ee5137430f56269cd3e6381ddf24cf46"; logging-data="272320"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19I+lliFNR3vBbRlq1FUfgN" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:d60zo64ireCbO95hAKIikIc+9Po= Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250506-6, 5/6/2025), Outbound message In-Reply-To: Bytes: 6049 On 5/6/2025 6:00 PM, Richard Damon wrote: > On 5/6/25 1:54 PM, olcott wrote: >> On 5/6/2025 6:06 AM, Richard Damon wrote: >>> On 5/5/25 10:29 PM, olcott wrote: >>>> On 5/5/2025 8:06 PM, Richard Damon wrote: >>>>> On 5/5/25 11:51 AM, olcott wrote: >>>>>> 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; >>>>>> } >>>>> >>>>> Which isn't a program until you include the SPECIFIC HHH that it >>>>> refutes, and thus your talk about correctly emulated by HHH is just >>>>> a lie. >>>>> >>>>>> >>>>>> 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. >>>>>> >>>>> >>>>> And *ITS INPUT*, for the HHH that answers 0, is the representation >>>>> of a program >>>> >>>> Not at all. This has always been stupidly wrong. >>>> The input is actually a 100% perfectly precise >>>> sequence of steps. With pathological self-reference >>>> some of these steps are inside the termination analyzer. >>>> >>> >>> Can't be, as the input needs to be about a program, which must, by >>> the definition of a program, include all its algorithm. >>> >>> Yes, there are steps that also occur in the termination analyzer, but >>> they have been effectively copied into the program the input describes. >>> >>> Note, nothing says that the representation of the program has to be >>> an assembly level description of it. It has to be a complete >>> description, that 100% defines the results the code will generate >>> (and if it will generate) but it doesn't need to be the exact >>> assembly code, >>> >>> YOU even understand that, as you present the code as "C" code, which >>> isn't assembly. >>> >>> What you forget is that the input program INCLUDES as its definiton, >>> all of the code it uses, and thus the call to the decider it is built >>> on includes that code into the decider, and that is a FIXED and >>> DETERMINDED version of the decider, the one that THIS version of the >>> input is designed to make wrong. >>> >>> This doesn't change when you hypothosize a different decider looking >>> at THIS input. >>> >> >> >>      If simulating halt decider H correctly simulates its >>      input D until H correctly determines that its simulated D >>      *would never stop running unless aborted* then >> >> *would never stop running unless aborted* >> Refers to a hypothetical HHH/DD pair of the same HHH that >> DD calls except that this hypothetical HHH never aborts. >> > > Right, but a correct simulation of D does halt, How the Hell is breaking the rules specified by the x86 language possibly correct? I could say that the sum of 5 + 7 is a dirty sock according to the rules of random gibberish. When I go by the rules of arithmetic I am proved wrong. DD emulated by HHH according to the rules of the x86 language that specify the HHH also emulates itself emulating DD until HHH determines that for the hypothetical HHH/DD pair where the hypothetical HHH never aborts DD would never stop running. If simulating halt decider H correctly simulates its input D until H correctly determines that its simulated D *would never stop running unless aborted* then *would never stop running unless aborted* refers to the hypothetical HHH/DD pair where HHH never aborts its simulation. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer