Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= Newsgroups: comp.theory Subject: Re: Turing Machine computable functions MUST apply finite string transformations to inputs Date: Thu, 1 May 2025 19:58:31 -0600 Organization: Christians and Atheists United Against Creeping Agnosticism Lines: 90 Message-ID: References: <87cyd5182l.fsf@nosuchdomain.example.com> <991dde3a60e1485815b789520c7149e7842d18f2@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 03:58:34 +0200 (CEST) Injection-Info: dont-email.me; posting-host="e60675c0bc32723a4a0575b8494fd739"; logging-data="4143968"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18ZicRubcyFkG6XHS9sqanH" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ggzzGesZq+n2tuh7U3YObXbojN0= Content-Language: en-US In-Reply-To: On 2025-05-01 19:09, olcott wrote: > On 5/1/2025 7:32 PM, André G. Isaak wrote: >> On 2025-05-01 14:15, olcott wrote: >>> On 5/1/2025 10:14 AM, André G. Isaak wrote: >>>> On 2025-04-30 21:50, olcott wrote: >>>>> On 4/30/2025 7:17 PM, André G. Isaak wrote: >>>> >>>>>> You are still hopelessly confused about your terminology. >>>>>> >>>>>> Computable functions are a subset of mathematical functions, and >>>>>> mathematical functions are *not* the same thing as C functions. >>>>>> Functions do not apply "transformations". They are simply >>>>>> mappings, and a functions which maps every pair of natural numbers >>>>>> to 5 is a perfectly legitimate, albeit not very interesting, >>>>>> function. >>>>>> >>>>>> What makes this function a *computable function* is that fact that >>>>>> it is possible to construct a C function (or a Turing Machine, or >>>>>> some other type of algorithm) such as int foo(int x, int y) >>>>>> {return 5;} which computes that particular function; but the C >>>>>> function and the computable function it computes are entirely >>>>>> separate entities. >>>>> >>>>> computes the sum of two integers >>>>> by transforming the inputs into an output. >>>>> int sum(int x, int y) { return x + y; } >>>>> >>>>> Computes no function because it ignores its inputs. >>>>> int sum(int x, int y) { return 5; } >>>> >>>> All you're demonstrating here is that you have no clue what a >>>> function is, nor, apparently, do you have any desire to learn. >>>> >>>> André >>>> >>> >>> What I am explaining is that a halt decider >>> must compute the mapping FROM THE INPUTS ONLY >>> by applying a specific set of finite string >>> transformations to the inputs. >> >> No. Halt deciders weren't even mentioned above. I was addressing your >> absurd claim that int foo(int x, int y) { return 5; } does not compute >> a function. This clearly indicates that you do not grasp the concept >> of "function". >> > > This is a brand new elaboration of computer > science that I just came up with. IOW something you've pulled out of your ass. > It is common knowledge THAT inputs must correspond > to OUTPUTS. What is totally unknown and brand new > created by me is HOW inputs are made to correspond > to OUTPUTS. We were discussing functions. Functions don't have inputs or outputs; they have domains and codomains. ALGORITHMS have inputs and outputs, and you keep conflating the two. > Specific finite string transformation rules are > applied to inputs to derive outputs. Please point to a definition of 'function' which mentions "finite string transformation rules". This may be a useful way of viewing some (but certainly not all) algorithms, but it has nothing to do with functions. Functions are simply a mapping from one set (the domain) to another set (the codomain) such that every element of the domain maps to one and only one element of the codomain. > What everyone else has been doing is simply GUESSING > that they correspond or relying on some authority > that say they must correspond. (Appeal to authority error). This is another baseless assertion that you've simply pulled out of your ass. If you think otherwise, please provide a concrete example > DD correctly emulated by HHH maps to NON-HALTING BEHAVIOR. > It really does, all that you have to do is PAY ATTENTION. Whether DD emulated by HH maps to halting or non-halting behaviour is entirely dependent on which function is being computed. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.