Path: ...!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: Is Richard a Liar? Date: Sun, 12 May 2024 10:58:02 -0500 Organization: A noiseless patient Spider Lines: 66 Message-ID: <v1qouc$2qb2s$1@dont-email.me> References: <v18e32$1vbql$1@dont-email.me> <v1dtdv$3dqg4$1@dont-email.me> <v1du2i$3dt7u$1@dont-email.me> <v1fetd$3s7jo$1@dont-email.me> <v1ft42$3vdau$2@dont-email.me> <-5Gdnf-nQvstC6b7nZ2dnZfqnPadnZ2d@brightview.co.uk> <v1gid8$4ilc$1@dont-email.me> <v1h9eu$9faf$1@dont-email.me> <v1iqli$nsva$1@dont-email.me> <v1k0ts$iuna$1@i2pn2.org> <v1k381$14mbi$2@dont-email.me> <v1labh$kf53$1@i2pn2.org> <v1lfnq$1e7af$1@dont-email.me> <v1lh1g$kf52$4@i2pn2.org> <v1lmo1$1g1mj$1@dont-email.me> <v1luu1$lbo5$3@i2pn2.org> <v1lvuo$1i47i$1@dont-email.me> <v1m1bf$lbo5$4@i2pn2.org> <v1m2hc$1ijhr$1@dont-email.me> <v1m31m$lbo4$1@i2pn2.org> <v1m4et$1iv85$1@dont-email.me> <v1m5co$lbo4$2@i2pn2.org> <v1m71h$1jnpi$1@dont-email.me> <v1m7mh$lbo5$5@i2pn2.org> <v1mb8f$1kgpl$1@dont-email.me> <v1mkf8$lbo5$7@i2pn2.org> <v1mkmm$1q5ee$1@dont-email.me> <v1na6f$1ugl0$1@dont-email.me> <v1o67n$24f4c$1@dont-email.me> <v1q1ie$2l40t$1@dont-email.me> <v1q9fp$qb0p$1@i2pn2.org> <v1qmq8$2prs6$1@dont-email.me> 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: <v1qmq8$2prs6$1@dont-email.me> 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