Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: Re: Defining a correct halting decidability decider Date: Sun, 11 Aug 2024 09:24:39 +0300 Organization: - Lines: 117 Message-ID: References: <0ec454016dab6f6d6dd5580f5d0eea49569293d8@i2pn2.org> <6ec9812649b0f4a042edd1e9a1c14b93e7b9a16b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 11 Aug 2024 08:24:39 +0200 (CEST) Injection-Info: dont-email.me; posting-host="cc6b6595fa10c51424bfd3c050efffdc"; logging-data="2287254"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19U+IHh5UT4avrly4gjjloz" User-Agent: Unison/2.2 Cancel-Lock: sha1:MHHoPkF6FHPZBXCY5eRJmkKLATM= Bytes: 5776 On 2024-08-10 11:03:31 +0000, olcott said: > On 8/10/2024 3:20 AM, Mikko wrote: >> On 2024-08-09 13:47:34 +0000, olcott said: >> >>> On 8/9/2024 3:56 AM, Mikko wrote: >>>> On 2024-08-08 13:21:57 +0000, olcott said: >>>> >>>>> On 8/8/2024 2:12 AM, Mikko wrote: >>>>>> On 2024-08-07 13:12:43 +0000, olcott said: >>>>>> >>>>>>> On 8/7/2024 1:59 AM, Mikko wrote: >>>>>>>> On 2024-08-04 19:33:36 +0000, olcott said: >>>>>>>> >>>>>>>>> On 8/4/2024 2:05 PM, Richard Damon wrote: >>>>>>>>>> On 8/4/24 2:49 PM, olcott wrote: >>>>>>>>>>> On 8/4/2024 1:38 PM, Richard Damon wrote: >>>>>>>>>>>> On 8/4/24 10:46 AM, olcott wrote: >>>>>>>>>>>>> When we define an input that does the opposite of whatever >>>>>>>>>>>>> value that its halt decider reports there is a way for the >>>>>>>>>>>>> halt decider to report correctly. >>>>>>>>>>>>> >>>>>>>>>>>>> int DD() >>>>>>>>>>>>> { >>>>>>>>>>>>>    int Halt_Status = HHH(DD); >>>>>>>>>>>>>    if (Halt_Status) >>>>>>>>>>>>>      HERE: goto HERE; >>>>>>>>>>>>>    return Halt_Status; >>>>>>>>>>>>> } >>>>>>>>>>>>> >>>>>>>>>>>>> int main() >>>>>>>>>>>>> { >>>>>>>>>>>>>    HHH(DD); >>>>>>>>>>>>> } >>>>>>>>>>>>> >>>>>>>>>>>>> HHH returns false indicating that it cannot >>>>>>>>>>>>> correctly determine that its input halts. >>>>>>>>>>>>> True would mean that its input halts. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> But false indicates that the input does not halt, but it does. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> I made a mistake that I corrected on a forum that allows >>>>>>>>>>> editing: *Defining a correct halting decidability decider* >>>>>>>>>>> 1=input does halt >>>>>>>>>>> 0=input cannot be decided to halt >>>>>>>>>> >>>>>>>>>> And thus, not a halt decider. >>>>>>>>>> >>>>>>>>>> Sorry, you are just showing your ignorance. >>>>>>>>>> >>>>>>>>>> And, the problem is that a given DD *CAN* be decided about halting, >>>>>>>>>> just not by HHH, so "can not be decided" is not a correct answer. >>>>>>>>> >>>>>>>>> A single universal decider can correctly determine whether >>>>>>>>> or not an input could possibly be denial-of-service-attack. >>>>>>>>> 0=yes does not halt or pathological self-reference >>>>>>>>> 1=no  halts >>>>>>>> >>>>>>>> Conventionally the value 0 is used for "no" (for example, no errors) >>>>>>>> and value 1 for "yes". If there are different "yes" results other >>>>>>> >>>>>>> A Conventional halt decider is 1 for halts and 0 for does not halt. >>>>>> >>>>>> That is because conventionally the question is "Does thing computation >>>>>> halt?" so "yes" means the same as "halts". >>>>>> >>>>>>> 0 also means input has pathological relationship to decider. >>>>>> >>>>>> It cannot mean both "does not halt" and "has pathological relationship >>>>>> to decider". Those two don't mean the same. >>>>>> >>>>>>> In other words 1 means good input and 0 means bad input. >>>>>> >>>>>> That is not the same in other words. >>>>>> >>>>>> An input is good in one sense if it specifies a computation and bad if >>>>>> it does not. In the latter case the decider is free to do anything as >>>>>> the input is not in its scope. >>>>>> >>>>>> In another sense an input is good if it is as the user wants it to be. >>>>>> If the user wants a non-halting computation then a halting one is bad. >>>>>> >>>>> >>>>> *Semantic property of well-behaved is decided for input* >>>>> It the program well behaved thus halts? >>>>> else The program is not well behaved. >>>> >>>> You don't need any meaning for "well-behaved". A program is good if >>>> it satisfies its purpose. >>> >>> https://en.wikipedia.org/wiki/Stipulative_definition >>> has_eaten_lunch is a Stipulative_definition defined below: >>> >>> A program is said to have the non trivial semantic >>> property of has_eaten_lunch when it halts and >>> ~has_eaten_lunch when it cannot be correctly determined >>> to halt. This defeat Rice's Theorem. >> >> that is not a useful stipulation. And there is no way to correctly >> determine that it is not possible to determine whether a computation >> halts. > > 1=halts > 0=does not halt or pathological relationship to decider Which does not use the stipulation and therefore does not demonstrate its usefulńess. That a computation has a pathological relationship to some decider does not prevent another partial haltdecider from determinig whther it halts. -- Mikko