Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Is Richard a Liar? Date: Sun, 12 May 2024 10:58:02 -0500 Organization: A noiseless patient Spider Lines: 66 Message-ID: References: <-5Gdnf-nQvstC6b7nZ2dnZfqnPadnZ2d@brightview.co.uk> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 12 May 2024 17:58:04 +0200 (CEST) Injection-Info: dont-email.me; posting-host="72ecece1a9bec17b694bf422ef8241f0"; logging-data="2960476"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/1AyLrg/fTA/2YL5NfPEs4" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:bk1N2jTyze4NtylqZKsBJjcDlQI= Content-Language: en-US In-Reply-To: Bytes: 4384 On 5/12/2024 10:21 AM, Mikko wrote: > On 2024-05-12 11:34:17 +0000, Richard Damon said: > >> On 5/12/24 5:19 AM, Mikko wrote: >>> On 2024-05-11 16:26:30 +0000, olcott said: >>> >>>> I am working on providing an academic quality definition of this >>>> term. >>> >>> The definition in Wikipedia is good enough. >>> >> >> I think he means, he is working on a definition that redefines the >> field to allow him to claim what he wants. > > Here one can claim whatever one wants anysay. > In if one wants to present ones claims on some significant forum then > it is better to stick to usual definitions as much as possible. > >> Sort of like his new definition of H as an "unconventional" machine >> that some how both returns an answer but also keeps on running. > > There are systems where that is possible but unsolvable problems are > unsolvable even in those systems. > When Ĥ is applied to ⟨Ĥ⟩ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn embedded_H is an actual UTM that has the extra feature of watching every state transition of its simulated input so that it detects the non-halting behavior pattern that we can all see. Execution trace of Ĥ applied to ⟨Ĥ⟩ (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to embedded_H (b) embedded_H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩ (c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process Simulation invariant: ⟨Ĥ⟩ correctly simulated by embedded_H never reaches its own simulated final state of ⟨Ĥ.qn⟩. (1) The directly executed embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to its own internal state of embedded_H.qn indicating that the correct and complete simulation of its input never halts. It never reaches Ĥ.qn. (2) embedded_H continues to simulate its input after it transitions to this internal state. (3) Each simulated embedded_H does the same thing. embedded_H is not a halt decider or a partial halt decider because all deciders are required to halt. embedded_H is not even a conventional termination analyzer for this same reason. None-the-less embedded_H does derive the correct halt status of its conventional HP input. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer