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Path: ...!weretis.net!feeder8.news.weretis.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: Sat, 1 Jun 2024 14:55:40 -0500 Organization: A noiseless patient Spider Lines: 102 Message-ID: <v3fubs$2ulbk$2@dont-email.me> References: <v3501h$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> <v3fqt9$2o13h$8@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 01 Jun 2024 21:55:41 +0200 (CEST) Injection-Info: dont-email.me; posting-host="5617c6a52e82e3edb2307f1199229213"; logging-data="3102068"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/8IVVRIXFg/e7U7EiHFgLM" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:EkpqYUcYyNU3VVhbqE3RrnwpgeU= In-Reply-To: <v3fqt9$2o13h$8@i2pn2.org> Content-Language: en-US Bytes: 5140 On 6/1/2024 1:56 PM, joes wrote: > Am Sat, 01 Jun 2024 09:52:54 -0500 schrieb olcott: >> 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: >>>>> > >>>>>> 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 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. >> >>>> 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? > I misunderstood this, too, but we want a single machine that solves the > problem on its own, not multiple that each solve parts. There could be > many such machines. > ∃H ∈ Turing_Machines is fulfilled when there are one or more machines that independently solve the halting problem. ∃!H ∈ Turing_Machines is ONLY fulfilled when there is exactly one machine that solves the halting problem. I knew what Linz meant from all the other proofs that I read. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer