Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: Re: Turing computable function for sum of two integers Date: Fri, 2 May 2025 11:15:34 +0300 Organization: - Lines: 80 Message-ID: References: <852f89c9196e0261b8156050fea4572fe886933f@i2pn2.org> <63af93cb608258cc3e12b9bab3a2efa0b7ee7eee@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 02 May 2025 10:15:34 +0200 (CEST) Injection-Info: dont-email.me; posting-host="cb793c8c3b892b6beb6c2827261db101"; logging-data="746813"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Y3/UutrhI4lKP9Ud4FwyD" User-Agent: Unison/2.2 Cancel-Lock: sha1:bhGfpMbmBtWtPV07+HXIg1VG1tQ= On 2025-04-30 17:36:44 +0000, olcott said: > On 4/29/2025 4:50 AM, Mikko wrote: >> On 2025-04-28 19:55:35 +0000, olcott said: >> >>> On 4/28/2025 11:01 AM, dbush wrote: >>>> On 4/28/2025 11:52 AM, olcott wrote: >>>>> On 4/28/2025 4:01 AM, Mikko wrote: >>>>>> On 2025-04-16 17:36:31 +0000, olcott said: >>>>>> >>>>>>> On 4/16/2025 7:29 AM, Richard Heathfield wrote: >>>>>>>> On 16/04/2025 12:40, olcott wrote: >>>>>>>>> sum(3,2) IS NOT THE SAME AS sum(5,2). >>>>>>>>> IT IS EITHER STUPID OR DISHONEST FOR YOU TO TRY TO >>>>>>>>> GET AWAY FOR CLAIMING THIS USING THE STRAW DECEPTION >>>>>>>>> INTENTIONALLY INCORRECT PARAPHRASE OF MY WORDS. >>>>>>>> >>>>>>>> Whether sum(3,2) is or is not the same as sum(5,2) is not the question. >>>>>>>> The question is whether a universal termination analyser can be >>>>>>>> constructed, and the answer is that it can't. >>>>>>>> >>>>>>>> This has been rigorously proved. If you want to overturn the proof >>>>>>>> you've got your work cut out to persuade anyone to listen, not least >>>>>>>> because anyone who tries to enter into a dialogue with you is met with >>>>>>>> contempt and scorn. >>>>>>>> >>>>>>>> The proof stands. >>>>>>>> >>>>>>> >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> >>>>>>> Not freaking allowed to look at any damn thing >>>>>>> else besides the freaking input. Must compute whatever >>>>>>> mapping ACTUALLY EXISTS FROM THIS INPUT. >>>>>> >>>>>> A halt decider is is not allowed to compute "whatever" mapping. It is >>>>>> required to compute one specific mapping: to "no" if the computation >>>>>> described by the input can be continesd forever without halting, to >>>>>> "no" otherwise. >>>>>> >>>>> >>>>> It must do this by applying the finite string transformation >>>>> rules specified by the x86 language to the input to HHH(DD). >>>>> >>>>> This DOES NOT DERIVE THE BEHAVIOR OF THE DIRECTLY EXECUTED DD. >>>>> It DOES DERIVE DD EMULATED BY HHH AND ALSO DERIVES THE RECURSIVE >>>>> EMULATION OF HHH EMULATING ITSELF EMULATING DD. >>>>> >>>> >>>> >>>> In other words, no H exists that satisfies the following requirements, >>> >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >> >> You have not proven that the requirements are wrong in any sense. > > int sum(int x, int y) { return 5; } > Is NOT a Turing Computable function for the sum of two integers. It is a Turing computable computable function of two integers. It is not the functiona that the vernacular term "sum" is usually understood to mean. > int sum(int x, int y) { x + y; } > Is a Turing Computable function for the sum of two integers. Right. But in order to compute the function the two integers and the value of the function must be reasonably encoded. -- Mikko