Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Turing Machine computable functions MUST apply finite string transformations to inputs Date: Wed, 30 Apr 2025 23:30:02 -0500 Organization: A noiseless patient Spider Lines: 74 Message-ID: References: <87cyd5182l.fsf@nosuchdomain.example.com> <991dde3a60e1485815b789520c7149e7842d18f2@i2pn2.org> <2430d330090ee702268894ff281eb444dc6a6a46@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 01 May 2025 06:30:03 +0200 (CEST) Injection-Info: dont-email.me; posting-host="426e05277e8812ec523191f9693f8994"; logging-data="1974399"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+H2HbyLtNyHhVbuP655690" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:HBgfCQ1nwq6EQGRtfVdlD96yMuI= X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250430-10, 4/30/2025), Outbound message Content-Language: en-US In-Reply-To: <2430d330090ee702268894ff281eb444dc6a6a46@i2pn2.org> On 4/30/2025 6:52 PM, Richard Damon wrote: > On 4/30/25 6:09 PM, olcott wrote: >> On 4/30/2025 2:55 PM, dbush wrote: >>> On 4/30/2025 1:32 PM, olcott wrote: >>>> On 4/30/2025 11:11 AM, Richard Heathfield wrote: >>>>> On 30/04/2025 16:44, joes wrote: >>>>>> Am Wed, 30 Apr 2025 10:09:45 -0500 schrieb olcott: >>>>>>> On 4/29/2025 5:01 AM, Mikko wrote: >>>>>> >>>>>>>> Irrelevant. There is sufficient agreement what Turing machines are. >>>>>>> >>>>>>> Turing machine computable functions must apply finite string >>>>>>> transformation rues to inputs to derive outputs. >>>>>>> >>>>>>> This is not a function that computes the sum(3,2): >>>>>>> int sum(int x, int y) { return 5; } >>>>>> Yes it is, for all inputs. >>>>> >>>>> Not much of a computation, though, is it? >>>>> >>>> >>>> It IS NOT a Turing Computable function >>> >>> Lying by misuse of terms. >>> >>> A turing computable function is a mapping for which an algorithm >>> exists to compute it, not the algorithm itself. >>> >>> Further use of "turing computable function" when what is meant is >>> "algorithm" will result in the former being replaced with the later >>> in future responses to your posts to make it clear what you are >>> actually talking about. >>> >>> >>>> because it does not ever apply any finite >>>> string transformation  rules to its inputs. >>> >>> Sure it does.  It computes the mapping of all pairs of integers to >>> the number 5. >>> >> >> int sum(int x, int y) { return 5; } >> Does not apply transformations to its inputs >> to derive its outputs thus is no kind of computable >> function not even for sum(2,3). >> > > And there is no requirement that a Turing Machine, or a Function, > actually use its input. > Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. *given an input of the function domain it can return the* *corresponding output* https://en.wikipedia.org/wiki/Computable_function Then the relation between the input and the output is violated. > Note sum(2,3) isn't a Function, it is an invocation of a Function. > > You seem to have a lot of misunderstanding about the meaning of the > words you use. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer