Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: HHH decides a non-trivial semantic property of its input Date: Thu, 8 Aug 2024 13:38:51 -0500 Organization: A noiseless patient Spider Lines: 83 Message-ID: References: <4-qdnbRw1Jw-Si37nZ2dnZfqlJwAAAAA@giganews.com> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 08 Aug 2024 20:38:51 +0200 (CEST) Injection-Info: dont-email.me; posting-host="7c97dfd2b0fa781dfb9291aeaceb4463"; logging-data="191742"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18klFxWkB77RTBCEkmi/3IZ" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:QqbyRWGVP/+IbmG0jXp2//+lo30= In-Reply-To: Content-Language: en-US Bytes: 4106 On 8/8/2024 2:17 AM, Mikko wrote: > On 2024-08-07 13:23:54 +0000, olcott said: > >> On 8/7/2024 2:06 AM, Mikko wrote: >>> On 2024-08-05 13:46:11 +0000, olcott said: >>> >>>> On 8/5/2024 8:44 AM, Python wrote: >>>>> Le 05/08/2024 à 13:50, olcott a écrit : >>>>>> On 8/5/2024 3:08 AM, Mikko wrote: >>>>>>> On 2024-08-04 14:46:02 +0000, olcott said: >>>>>>> >>>>>>>> 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. >>>>>>> >>>>>>> That is called a "partial halt decider". The set of requirements is >>>>>>> a subset of the requirements for "halt decider" but still require >>>>>>> that the answer is not "halts" if the input does not halt and that >>>>>>> the answer is not "does not halt" if the input halts. The difference >>>>>>> is that a "halt decider" is required to give one of these answers >>>>>>> for every input but a "partial halt decider" is not. >>>>>>> >>>>>>> For every computation there is a partial halt decider that >>>>>>> answers it. >>>>>>> >>>>>> >>>>>> I call it a halting decidability decider. >>>>>> 1=input halts >>>>>> 0=input does not halt or has pathological relationship with its >>>>>> decider >>>>> >>>>> So it is NOT an halt decider. Case closed. You've lost your time >>>>> for years, and made a lot of people lose their time too. >>>>> >>>>> >>>>> >>>> >>>> It refutes Rice >>> >>> No, it does not. Nothing is refuted as long as you have not proven >>> anything. >>> >> >> 1 = halts = good input = decidable >> 0 = (not halts or pathological) = bad input = not decidable as halting >> HHH decides a non-trivial semantic property of its input. > > Your "not decidable as halting" is not a property of input. Another > partial decider may be able to determine that the input is halting > and therefore decidable as halting. > https://en.wikipedia.org/wiki/Stipulative_definition The stipulative definition of the semantic property has_not_ate_lunch_yet means that the input halts and ~has_not_ate_lunch_yet means the input cannot be determined to halt. This is can be used to detect and reject denial of service attacks that have targeted the detector. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer