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Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon <richard@damon-family.org> Newsgroups: comp.theory,sci.logic Subject: Re: A computable function that reports on the behavior of its actual self is not allowed Date: Mon, 13 May 2024 20:30:14 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <v1ubam$v37v$8@i2pn2.org> 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> <v1rlto$324ln$3@dont-email.me> <v1rnfg$qvg3$13@i2pn2.org> <v1tlmd$3k599$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 14 May 2024 00:30:14 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1019135"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <v1tlmd$3k599$1@dont-email.me> X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 9115 Lines: 210 On 5/13/24 2:20 PM, olcott wrote: > On 5/12/2024 7:39 PM, Richard Damon wrote: >> On 5/12/24 8:12 PM, olcott wrote: >>> 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. >> >> It isn't even a "program" per the term-of-the-art, since it generates >> and answer without ending, thus your "proof" is based on lies. >> > > I have no idea what you are basing this on, a "program" > is not any term-of-the-art of the theory of computation. Then why is one phrasing of the Halting Problem about the decider answering about the "program" given to it? I guess you just don't understand what the terms mean. > > It is well known in the field that some Turing Machines > never halt, so it certainly can be a Turing machine. Yes, but it doesn't ANSWER. Remember the definition of a decider, > > You are certainly correct that it is not a computable > function. So, you AGREE that you 20 year quest to show that Turing was WRONG about Halting not being a computable function, as we can not build an always correct Halt Decider? > > We can say that H is proven to "know" the correct halt > status, yet cannot "say" the correct halt status in the > conventional way. But that isn't what Computation Theory is about. > > Objectively this does seem to be a significant breakthrough > over both YES and NO are the wrong answer from H. I don't > think that you can provide any correct reasoning to the contrary. Nope. And Yes and No are not both wrong, Which ever answer that H gives is wrong, and the other is right. You don't seem to understand that a given H will ALWAYS give the same answer to the same input, and thus only one answer needs to be wrong. > > *RHETORIC COUNTS AS ZERO REASONING* > *RHETORIC COUNTS AS ZERO REASONING* > *RHETORIC COUNTS AS ZERO REASONING* Right, like what you use. Note, I intersperse my "Rhetoric" with facts, unlike you. > >>> >>>> 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. >>> >> >> Where? >> >> You claimed the equivalent of a cat being a 10 story office building. >> ========== REMAINDER OF ARTICLE TRUNCATED ==========