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: Turing Machine computable functions MUST apply finite string transformations to inputs Date: Wed, 30 Apr 2025 23:26:16 -0500 Organization: A noiseless patient Spider Lines: 71 Message-ID: References: <87cyd5182l.fsf@nosuchdomain.example.com> <991dde3a60e1485815b789520c7149e7842d18f2@i2pn2.org> <75dbea539a8ea52ccf39e37eb2f69737c1df5c12@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 06:26:16 +0200 (CEST) Injection-Info: dont-email.me; posting-host="426e05277e8812ec523191f9693f8994"; logging-data="1974399"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+NIdP9RBevdOBurt2lsMCr" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:vexp7cU20vsYkt0E7AdAtoA7hsE= In-Reply-To: <75dbea539a8ea52ccf39e37eb2f69737c1df5c12@i2pn2.org> Content-Language: en-US X-Antivirus: Norton (VPS 250430-10, 4/30/2025), Outbound message X-Antivirus-Status: Clean Bytes: 4118 On 4/30/2025 6:50 PM, Richard Damon wrote: > On 4/30/25 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 >> because it does not ever apply any finite >> string transformation  rules to its inputs. >> >> THE OUTPUTS MUST CORRESPOND TO THE INPUTS. >> sum(4,3) returns 5 proving that sum is >> not a Turing Computable function. >> > > Sure it is. You just don't know that that mean. > Computable functions must apply finite string transformations to inputs. sum does not do that. > THe function given computes the Computable Function defined by the > mapping of all pair (x, y) -> the value 5. > > That is a perfectly fine Function, and easily proved to be computable. > > It isn't a correct function for computing the addition function that > maps the pair (x, y) -> x+y, but that wasn't what you said, because you > don't know what you are talking about. > > You don't seem to understand that "Functions" are defined just by the > input -> output mapping that they specify. > > They are Computable if some Turing Machine exists that can create that > whole mapping (via some representation method for the inputs/outputs) > > But the "Computable Function" still isn't defined by the code fo that > Turing Machine, but by the mapping. > > NO "Turing Machine" is a "Turing Computable Function" as they are > different categories of things. > > Turing Machine as strictly defined by the rules that they are built on > that create the mappings they compute. > > Functions (Computable or Not) are defined by the Mapping of Input to > Output that they are. > > > Turing Machine COMPUTE some Computable Function, they are not the > Function itself. > > -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer