Path: ...!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: Correcting the definition of the halting problem --- Computable functions Date: Mon, 24 Mar 2025 17:11:38 -0500 Organization: A noiseless patient Spider Lines: 71 Message-ID: References: <30c2beae6c191f2502e93972a69c85ff227bfd03@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 24 Mar 2025 23:11:39 +0100 (CET) Injection-Info: dont-email.me; posting-host="ac1d39214123a2f0a8db335464f421b3"; logging-data="1945278"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+6NMdY1KA6wa0Hp+NwzDVZ" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:9OBhQSMR2nEmFk/oqKu0VMAosm0= In-Reply-To: X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250324-4, 3/24/2025), Outbound message Content-Language: en-US Bytes: 4664 On 3/24/2025 3:18 PM, dbush wrote: > On 3/24/2025 4:11 PM, olcott wrote: >> On 3/24/2025 12:35 PM, dbush wrote: >>> On 3/24/2025 12:44 PM, olcott wrote: >>>> On 3/24/2025 10:14 AM, dbush wrote: >>>>> On 3/24/2025 11:03 AM, olcott wrote: >>>>>> On 3/24/2025 6:23 AM, Richard Damon wrote: >>>>>>> On 3/23/25 11:09 PM, olcott wrote: >>>>>>>> It is impossible for HHH compute the function from the direct >>>>>>>> execution of DDD because DDD is not the finite string input >>>>>>>> basis from which all computations must begin. >>>>>>>> https://en.wikipedia.org/wiki/Computable_function >>>>>>> >>>>>>> WHy isn't DDD made into the correct finite string?i >>>>>>> >>>>>> >>>>>> DDD is a semantically and syntactically correct finite >>>>>> stirng of the x86 machine language. >>>>> >>>>> Which includes the machine code of DDD, the machine code of HHH, >>>>> and the machine code of everything it calls down to the OS level. >>>>> >>>>>> >>>>>>> That seems to be your own fault. >>>>>>> >>>>>>> The problem has always been that you want to use the wrong string >>>>>>> for DDD by excluding the code for HHH from it. >>>>>>> >>>>>> >>>>>> DDD emulated by HHH directly causes recursive emulation >>>>>> because it calls HHH(DDD) to emulate itself again. HHH >>>>>> complies until HHH determines that this cycle cannot >>>>>> possibly reach the final halt state of DDD. >>>>>> >>>>> >>>>> Which is another way of saying that HHH can't determine that DDD >>>>> halts when executed directly. >>>>> >>>> >>>> given an input of the function domain it can >>>> return the corresponding output. >>>> https://en.wikipedia.org/wiki/Computable_function >>>> >>>> Computable functions are only allowed to compute the >>>> mapping from their input finite strings to an output. >>>> >>> >>> >>> The HHH you implemented is computing *a* computable function, but >>> it's not computing the halting function: >>> >> >> The whole point of this post is to prove that >> no Turing machine ever reports on the behavior >> of the direct execution of another Turing machine. >> > > Sure it can.  Any that takes a description of a turning machine that > halt when executed directly is It has no way of directly computing this. It can only compute the behavior that the finite string specifies. > correct to return 1, regardless of the > logic used to do so. > > -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer