Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: comp.theory Subject: Re: Unpartial Halt Deciders --- category error Date: Tue, 22 Apr 2025 13:02:32 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: <87zfgdnufj.fsf@nosuchdomain.example.com> <0JxMP.1398486$cgs7.284882@fx14.ams4> <87sem5nu3q.fsf@nosuchdomain.example.com> <438052adf5074f27313bbb52c9f14c20fcfa2418@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Tue, 22 Apr 2025 13:02:32 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1373013"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Am Sat, 19 Apr 2025 15:44:31 -0500 schrieb olcott: > On 4/19/2025 1:06 PM, Mr Flibble wrote: >> On Sat, 19 Apr 2025 13:34:40 -0400, Richard Damon wrote: >>> On 4/19/25 8:05 AM, Mr Flibble wrote: >>>> On Sat, 19 Apr 2025 07:55:55 -0400, Richard Damon wrote: >>>>> On 4/18/25 11:52 PM, olcott wrote: >>>>>> On 4/18/2025 2:32 PM, Keith Thompson wrote: >>>>>>> Mr Flibble writes: >>>>>>>> On Fri, 18 Apr 2025 12:25:36 -0700, Keith Thompson wrote: >>>>>>>>> Mr Flibble writes: >>>>>>>>>> I, aka Mr Flibble, have created a new computer science term, >>>>>>>>>> the "Unpartial Halt Decider".  It is a Halt Decider over the >>>>>>>>>> domain of all program-input pairs excluding pathological input >>>>>>>>>> (a manifestation of the self referencial category error). >>>>>>>>> [...] >>>>>>>>> >>>>>>>>> Do you have a rigorous definition of "pathological input"? >>>>>>>>> Is there an algorithm to determine whether a given input is >>>>>>>>> "pathological" or not? >>>>>>>>> I could define an is_prime() function like this: >>>>>>>>> >>>>>>>>>      bool is_prime(int n) { >>>>>>>>>          return n >= 3 && n % 2 == 1; >>>>>>>>>          // returns true for odd numbers >= 3, false >>>>>>>>>          for all others >>>>>>>>>      } >>>>>>>>> I'll just say that odd numbers that are not prime are >>>>>>>>> pathological input, so I don't have to deal with them. >>>>>>>> >>>>>>>> Pathological input: Self-referencial to the decider. >>>>>>> >>>>>>> Do you have a *rigorous* definition of "pathological input"? >>>>>>> Is there an algorithm to determine whether a given input is >>>>>>> "pathological" or not? >>>>>>> >>>>>> int DD() >>>>>> { >>>>>>   int Halt_Status = HHH(DD); >>>>>>   if (Halt_Status) >>>>>>     HERE: goto HERE; >>>>>>   return Halt_Status; >>>>>> } >>>>>> Patterns isomorphic to the above when simulated by HHH. >>>>>> >>>>> Examples are not definitions. >>>>> And the problem is that the above example is itself a category error >>>>> for the problem, as the DD provided above isn't a complete program, >>>>> as it doesn't include the code for HHH as required, and when you >>>>> include Halt7.c as part of the input, your HHH isn't a seperate >>>>> program of its own, and thus doesn't have a Turing Complete range of >>>>> inputs it can accept. >>>> >>>> Ah, the fundamental mistake you have been making all this time, >>>> Damon! >>>> The self-referencial category error doesn't magically disappear by >>>> providing source code rather than a run-time function address to the >>>> decider; you are simply transforming the same input without affecting >>>> the result. >>> >>> And WHAT is the category error? You stil can't show the difference in >>> CATEGORY between what is allowed and what isn't, and in fact, you >>> can't even precisely define what is and isn't allowed. >>> Now, you also run into the issue that the "Olcott System" begins with >>> an actual category error as we do not have the required two seperate >>> programs of the "Decider" and the "Program to be decided on" given via >>> representation as the input, as what you want to call that program to >>> be decided isn't one without including the code of the decider it is >>> using, >>> and when you do include it, the arguments about no version of the >>> decider being able to succeed is improper as it must always be that >>> exact program that we started with, and thus it just FAILS to do a >>> correct simulation, while a correct simulation of this exact input >>> (which includes the ORIGINAL decider) will halt. >> >> The category error is extant over the domain of pathological inputs, no >> matter what form those inputs take. > > The category error in the halting problem proof is to define an input D > that is able to actually do the opposite of whatever value that H > reports. > Now the question: Does the input D halt becomes self-contradictory for > H. > So it is asking a yes/no question where both yes and no are the wrong > answer that is the category error. No, D either halts or doesn't depending on H (which must return a value). And H can't turn around and return the other value, as that changes D. There are other deciders that get D right, but the same construction works on them: every supposed decider has a counterexample, none decides every input. -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.