Deutsch English Français Italiano |
<v3hu4u$3bkv5$8@dont-email.me> View for Bookmarking (what is this?) Look up another Usenet article |
Path: ...!feeds.phibee-telecom.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: comp.theory Subject: Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets Date: Sun, 2 Jun 2024 09:04:14 -0500 Organization: A noiseless patient Spider Lines: 143 Message-ID: <v3hu4u$3bkv5$8@dont-email.me> References: <v3501h$lpnh$1@dont-email.me> <v3ci7v$283tt$1@dont-email.me> <v3cr8n$29gdk$2@dont-email.me> <v3eljo$2migl$1@dont-email.me> <v3fck6$2qsgd$3@dont-email.me> <v3ha76$39brb$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 02 Jun 2024 16:04:15 +0200 (CEST) Injection-Info: dont-email.me; posting-host="3e1a2626012d6c432c11247ed1bf0353"; logging-data="3527653"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+2Qh+R1HCcqK3YD0o9q27k" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Lt3TbeJ6irIwXoTwBFN/9fGd/i8= In-Reply-To: <v3ha76$39brb$1@dont-email.me> Content-Language: en-US Bytes: 6638 On 6/2/2024 3:24 AM, Mikko wrote: > On 2024-06-01 14:52:54 +0000, olcott said: > >> On 6/1/2024 3:20 AM, Mikko wrote: >>> On 2024-05-31 15:44:22 +0000, olcott said: >>> >>>> On 5/31/2024 8:10 AM, Mikko wrote: >>>>> On 2024-05-28 16:16:48 +0000, olcott said: >>>>> >>>>>> typedef int (*ptr)(); // ptr is pointer to int function in C >>>>>> 00 int H(ptr p, ptr i); >>>>>> 01 int D(ptr p) >>>>>> 02 { >>>>>> 03 int Halt_Status = H(p, p); >>>>>> 04 if (Halt_Status) >>>>>> 05 HERE: goto HERE; >>>>>> 06 return Halt_Status; >>>>>> 07 } >>>>>> 08 >>>>>> 09 int main() >>>>>> 10 { >>>>>> 11 H(D,D); >>>>>> 12 return 0; >>>>>> 13 } >>>>>> >>>>>> When Ĥ is applied to ⟨Ĥ⟩ >>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>>>> >>>>>> *Formalizing the Linz Proof structure* >>>>>> ∃H ∈ Turing_Machines >>>>>> ∀x ∈ Turing_Machines_Descriptions >>>>>> ∀y ∈ Finite_Strings >>>>>> such that H(x,y) = Halts(x,x) >>>>>> >>>>>> *Here is the same thing applied to H/D pairs* >>>>>> ∃H ∈ C_Functions >>>>>> ∀D ∈ x86_Machine_Code_of_C_Functions >>>>>> such that H(D,D) = Halts(D,D) >>>>>> >>>>>> In both cases infinite sets are examined to see >>>>>> if any H exists with the required properties. >>>>> >>>>> That says nothing about correct simulation. It says >>>>> something abuout some D but not whether it is correctly >>>>> simulated. Also nothing is said about templates or >>>>> infinite sets. At the end is claimed that some >>>>> infinite sets are examined but not who examined, nor >>>>> how, nor what was found in the alleged examination. >>>>> >>>> >>>> *Formalizing the Linz Proof structure* >>>> ∃H ∈ Turing_Machines >>>> ∀x ∈ Turing_Machines_Descriptions >>>> ∀y ∈ Finite_Strings >>>> such that H(x,y) = Halts(x,x) >>> >>> The above is the counter hypothesis for the proof. Proof structore >>> is that a contradiction is derived from the counter hypthesis. >>> >>>> The above disavows Richard's claim based on a misinterpretation of >>>> Linz that the Linz proof is about a single specific Turing machine. >>> >>> Your ∃H declares H as a new symbol for a specific Turing machine. >>> Therefore everything that follows refers to that specific Turing >>> machine. >>> There may be others that could be discussed the same way but they >>> aren't. >>> >> >> ∃H ∈ Turing_Machines >> There exists at least one H >> from the infinite set of all Turing_Machines >> >> ∃!H ∈ Turing_Machines >> There exists a single unique H >> from the infinite set of all Turing_Machines > > The symbol ∃! is non-standard and should be defined when used. > > And there is no point to present some formulas without saying > anything about them. > >>>> The domain of this problem is to be taken as the set of >>>> all Turing machines and all w; that is, we are looking >>>> for a single Turing machine that, given the description >>>> of an arbitrary M and w, will predict whether or not the >>>> computation of M applied to w will halt. >>> >>> Note the words "a single Turing machine". >> >> I know that he said that yet he meant this >> ∃H ∈ Turing_Machines *and didn't mean this* ∃!H ∈ Turing_Machines >> or he would be contradicting every other HP proof. > > He didn't mean either. Your false claim is merely an attempted > preparation of strawman deception. > >>>> Linz <IS NOT> looking for a single machine that gets the wrong answer. >>>> Linz is looking for at least one Turing Machine that gets the right >>>> answer: ∃H ∈ Turing_Machines >>> >>> Not at least one but exactly one. The Halting Problem asks for one >>> or a proof that there is none. >> >> In other words when there are two machines that solve the halting >> problem then the halting problem IS NOT SOLVED? > > If there are two then one of them is one and the other is irrelevant. ∃!H ∈ Turing_Machines ∀x ∈ Turing_Machines_Descriptions ∀y ∈ Finite_Strings such that H(x,y) = Halts(x,x) https://en.wikipedia.org/wiki/Uniqueness_quantification He was saying that Linz was saying that Linz was looking for exactly one unique Turing machine that solved the halting problem. > When Linz says "we are looking for a single Turing machine that ..." > he implies that when he (or someone) finds one he is not going to > look for another one. When he finally proves that it is not possible > to find one it is obvious that it is not possible to find more. > > And if you need to ask that you don't need to as why you look stupid. > Unless we attain 100% perfectly identical encoding and decoding of meanings the truth of what I am saying with slip through the cracks of ambiguity. ∃H ∈ Turing_Machines ∀x ∈ Turing_Machines_Descriptions ∀y ∈ Finite_Strings such that H(x,y) = Halts(x,x) Does there exist at least one H that solves the halting problem? -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer