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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: comp.theory,sci.logic Subject: Re: A computable function that reports on the behavior of its actual self is not allowed Date: Sun, 12 May 2024 19:12:40 -0500 Organization: A noiseless patient Spider Lines: 104 Message-ID: <v1rlto$324ln$3@dont-email.me> References: <v1r566$2uo21$1@dont-email.me> <v1rbmu$305vp$1@dont-email.me> <v1rcvn$qvg3$9@i2pn2.org> <v1rfcn$311mk$1@dont-email.me> <v1rggf$qvg3$10@i2pn2.org> <v1rigu$31mqu$1@dont-email.me> <v1rl16$qvg2$5@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 13 May 2024 02:12:41 +0200 (CEST) Injection-Info: dont-email.me; posting-host="822a7b45c10435b9354ed3bfb60d5b64"; logging-data="3216055"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19GLfk8xQdMAJ0x4FaUNpa6" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:DNwR4sDoeprTX0GfoGn8GcJNPI8= In-Reply-To: <v1rl16$qvg2$5@i2pn2.org> Content-Language: en-US Bytes: 5593 On 5/12/2024 6:57 PM, Richard Damon wrote: > On 5/12/24 7:14 PM, olcott wrote: >> On 5/12/2024 5:40 PM, Richard Damon wrote: >>> On 5/12/24 6:21 PM, olcott wrote: >>>> On 5/12/2024 4:40 PM, Richard Damon wrote: >>>>> On 5/12/24 5:18 PM, olcott wrote: >>>>>> On 5/12/2024 2:27 PM, olcott wrote: >> >>>>>>> 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 >>>>>>> >>>>>>> A computable function that reports on the behavior of its actual >>>>>>> self (or reports on the behavior of its caller) is not allowed. >>>>>>> >>>>>>> A decider must halt whereas simulating a pathological input >>>>>>> that would never halt unless aborted can only halt by aborting. >>>>>>> >>>>>>> This causes the direct execution of this input after it has been >>>>>>> aborted >>>>>>> to have different behavior than the simulated input that cannot >>>>>>> possibly >>>>>>> stop running unless aborted. >>>>>>> >>>>>> >>>>>> *MORE PRECISE WORDING* (this may take a few more rewrites) >>>>>> When Ĥ is applied to ⟨Ĥ⟩ >>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>>>> >>>>>> It is a verified fact that the directly executed Ĥ ⟨Ĥ⟩ cannot >>>>>> possibly >>>>>> stop running unless simulating partial halt decider embedded_H aborts >>>>>> its simulation of its input. >>>>> >>>>> But since embedded_H implements a specific algorithm, either it >>>>> will or it won't. "unless" is a meaningless word here, it implies a >>>>> case that can't happen. >>>>> >>>>> We can look at the two possible cases. >>>>> >>>>> First, if embedded_H doesn't ever abort its simulation, then, as >>>>> you have desceribed, THAT embedded_H creates a H^ that will never >>>>> halt, but the H that was based on will also never abort its >>>>> simulation (or you lied that embedded_H is the needed copy of H) >>>>> and thus never answer and fail to be a decider. >>>>> >>>> >>>> It can answer without halting by transitioning to its own internal >>>> non-final state of embedded_H.qn without ever reaching Ĥ.qn. Every >>>> simulated instance of embedded_H would do this same thing and then >>>> continue simulating its input. >>> So, you just don't understand how algorithms work, and how >>> compuations are DEFINED. >>> >>> >>> If you want to try to define a new system of compuation that allows >>> giving answer without the algorithm ending, but still allows all the >>> composition operations that are included in computation theory, go >>> ahead and try. >>> >>> You then need to show that it is Turing Complete, which means that >>> you can't outlaw any computation allowed in a Turing Machine, like H^. >>> >> >> *It <is> a way for embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to get the correct answer* >> *It <is> a way for embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to get the correct answer* >> *It <is> a way for embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to get the correct answer* > > Nope. > > Claiming to do something that isn't the way defined doesn't make it work. > It is not a halt decider. It is not even a termination analyzer. It <is> an huge improvement over both YES and NO from H are the wrong answer. NO from H IS THE CORRECT ANSWER. > That it like claiming you can make you cat bark, by trying to call your > dog a cat. > >> >> Every prior work that I have ever seen and probably every prior >> work that exists essentially concludes that both YES and NO are the >> wrong answer for H to provide for every H/D pair where H and D have >> the HP pathological relationship. > > Which ever answer H gives, will be wrong. > I JUST PROVED OTHERWISE. YES IS THE CORRECT ANSWER AND AS LONG AS H PROVIDES THIS ANSWER WITHOUT STOPPING NOTHING CONTRADICTS IT. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer