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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: dbush Newsgroups: comp.theory Subject: Re: Correcting the definition of the halting problem --- Computable functions Date: Tue, 25 Mar 2025 10:45:57 -0400 Organization: A noiseless patient Spider Lines: 89 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: Tue, 25 Mar 2025 15:45:58 +0100 (CET) Injection-Info: dont-email.me; posting-host="558cb3f1e92ebc1bf3f45b6c0d288267"; logging-data="3724739"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/hI1diFDWnvu7ulqg2YEby" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:vnxSgIT4D4sM7e+pJtuToJVViRc= Content-Language: en-US In-Reply-To: Bytes: 5145 On 3/24/2025 11:29 PM, olcott wrote: > On 3/24/2025 10:12 PM, dbush wrote: >> On 3/24/2025 10:07 PM, olcott wrote: >>> On 3/24/2025 8:46 PM, André G. Isaak wrote: >>>> On 2025-03-24 19:33, olcott wrote: >>>>> On 3/24/2025 7:00 PM, André G. Isaak wrote: >>>> >>>>>> In the post you were responding to I pointed out that computable >>>>>> functions are mathematical objects. >>>>> >>>>> https://en.wikipedia.org/wiki/Computable_function >>>>> >>>>> Computable functions implemented using models of computation >>>>> would seem to be more concrete than pure math functions. >>>> >>>> Those are called computations or algorithms, not computable functions. >>>> >>> >>> https://en.wikipedia.org/wiki/Pure_function >>> Is another way to look at computable functions implemented >>> by some concrete model of computation. >>> >> >> And not all mathematical functions are computable, such as the halting >> function. >> >>>> The halting problems asks whether there *is* an algorithm which can >>>> compute the halting function, but the halting function itself is a >>>> purely mathematical object which exists prior to, and independent >>>> of, any such algorithm (if one existed). >>>> >>> >>> None-the-less it only has specific elements of its domain >>> as its entire basis. For Turing machines this always means >>> a finite string that (for example) encodes a specific >>> sequence of moves. >> >> False.  *All* turing machine are the domain of the halting function, >> and the existence of UTMs show that all turning machines can be >> described by a finite string. >> > > You just aren't paying enough attention. Turing machines > are never in the domain of any computable function. > > False. The mathematical function that counts the number of instructions in a turing machine is computable. >>> >>> The math halting function is free to "abstract away" key >>> details that change everything. That is why I have never >>> been talking about the pure math and have always been >>> referring to its implementation in a model of computation. >>> >> >> There are no details abstracted away.  The halting function is simply >> uncomputable. >> > > When the measure of the behavior specified by a > finite string input DD is when correctly emulated > by HHH then DD can't reach its own final halt state > then not-halting is decidable. > That's not non-halting, that's not-PO-halting. Halting, as currently defined, is not decidable. When the measure of the behavior specified by a finite string input DD is when directly executed then DD halts and HHH doesn't report that. >>> A halt decider cannot exist >> >> So again, you explicitly agree with the Linz proof and all other >> proofs of the halting function. >> >>> because the halting problem is defined incorrectly >> >> There's nothing incorrect about wanting something that would solve the >> Goldbach conjecture and make unknowable truths knowable.  Your >> alternate definition won't provide that. >> >> There's no requirement that a function be computable. > >