Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: Incorrect requirements --- Computing the mapping from the input to HHH(DD) Date: Sat, 10 May 2025 19:04:26 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: <87msbmeo3b.fsf@nosuchdomain.example.com> <875xiaejzg.fsf@nosuchdomain.example.com> <87jz6qczja.fsf@nosuchdomain.example.com> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 10 May 2025 23:18:54 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="4004157"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US On 5/10/25 4:26 PM, olcott wrote: > On 5/10/2025 3:07 PM, Alan Mackenzie wrote: >> Mr Flibble wrote: >>> On Sat, 10 May 2025 18:48:12 +0000, Alan Mackenzie wrote: >> >>>> olcott wrote: >>>>> On 5/10/2025 7:37 AM, Bonita Montero wrote: >> >>>> [ .... ] >> >>>>>> I guess that not even a professor of theoretical computer science >>>>>> would spend years working on so few lines of code. >> >> >>>>> I created a whole x86utm operating system. >>>>> It correctly determines that the halting problem's otherwise >>>>> "impossible" input is actually non halting. >> >>>> You've spent over 20 years on this matter.  Compare this with Alan >>>> Turing's solution of the Entscheidungsproblem.  He published this in >>>> 1936 when he was just 24 years old. >> >>> Turing didn't solve anything: what he published contained a mistake: the >>> category (type) error that I have described previously in this forum. >> >> What arrogant self-important ignorance!  Turing indeed solved the >> Entscheidungsproblem.  His procedure has been verified by hundreds of >> thousands of mathematicians over the last century, and none of them have >> found flaws in it. >> >> It is overwhelmingly likely that your lack of mathematical training has >> led you to delude yourself about finding an error.  The same applies to >> Peter Olcott. >> >>> /Flibble >> > > Once we understand that functions computed > by models of computation must apply the sequence > of steps of an algorithm to derive their output > from their input then we have one key element. Yes, but non-computable functions do not. > > Then we also need to understand that termination > analyzers are required to compute the mapping from > this input to the behavior ACTUALLY SPECIFIED by > this input. And that behavior is SPECIFIED as the behavior of the program their input represents when it is actually run, (with any and all input for a termination analyser) > > The last step is understanding is that computing > the mapping to the behavior specified by this > input finite string must be according to the > model's computation language. Only what the computation the generates, not the mapping for the CORRECT answer. > > This means that HHH is correct to reject its > input DD because DD emulated by HHH according > to the rules of the x86 language specifies > recursive emulation (non halting behavior). Nope. As the input represents a program that will HALT since the decider it uses says it will not halt. Of course, this requires that you actually built a program as the input, and as the decider, and thus they both have fixed behavior. That means that when we correctly emulate that D, it *WILL* use the algorithm form the H that returned non-halting, and thus get that answer and thus halt. THe fact that H's incorrect emulation didn't get there is irrelevent. > > *Likewise for the Linz Proof* > > When Ĥ is applied to ⟨Ĥ⟩ > Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ > Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn > > (a) Ĥ copies its input ⟨Ĥ⟩ > (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ > (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩  ... > > ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly > ever reach its own simulated final state ⟨Ĥ.qn⟩ > But ⟨Ĥ⟩ isn't correctly simulated by embedded_H, as the H that it is a copy of has been said to abort and go to qn, is it will also. You are just showing that you believe it is ok to lie in your logic.