Path: ...!2.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: =?UTF-8?Q?Re=3A_Working_out_the_details_of_the_steps_of_=C4=A4=2EH_?= =?UTF-8?B?4p+oxKTin6kg4p+oxKTin6kgPMSkPiDiiqIqIMSkLkhxbg==?= Date: Sun, 10 Mar 2024 09:41:45 -0500 Organization: A noiseless patient Spider Lines: 73 Message-ID: References: <9YIGN.461274$c3Ea.142857@fx10.iad> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 10 Mar 2024 14:41:47 -0000 (UTC) Injection-Info: dont-email.me; posting-host="27c523feaef98dc1b326600190c611c0"; logging-data="3172008"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+j1LNX0FzI9YUAlo5MuQI0" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:/g9ySaI7G2TRd6JncpkWClTm/5A= Content-Language: en-US In-Reply-To: Bytes: 5037 On 3/10/2024 7:39 AM, Mikko wrote: > On 2024-03-09 15:44:02 +0000, olcott said: > >> On 3/9/2024 3:32 AM, Mikko wrote: >>> On 2024-03-08 21:34:30 +0000, olcott said: >>> >>>> Olcott machines are fully specified. Some of the details of the >>>> exact steps that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> would use to detect that it must >>>> abort the simulation of it input to prevent is own infinite >>>> execution must be worked out. >>> >>> What is the difference between ⟨Ĥ⟩ and <Ĥ> above and on the >>> subject line? >>> >> >> We know in advance that every Turing Machine Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn >> is the correct answer when all simulating halt deciders would >> correctly report on the behavior of their input from their own POV. >> >> I created Olcott machines to make it easier to see how Ĥ.H would >> do this. It may be the case that a Turing machine Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can >> detect that it must abort its simulation, thus from its own POV >> its input does not halt. For whatever reason that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn >> H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy would be correct. >> >> Instead of Olcott machines we can simply hypothesize that >> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is somehow able to detect that its input would not >> halt from its own POV and thus must abort the simulation of >> its input and transition to Ĥ.Hqn. This makes it obvious >> that H ⟨Ĥ⟩ ⟨Ĥ⟩ has the basis to transition to H.qy. >> >> This was not possible before the Olcott notion of simulating >> halt deciders that correctly determine the halt status of their >> inputs from their own POV. Previously Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ had no basis >> to report anything. As soon as it does have some basis to report >> something then H ⟨Ĥ⟩ ⟨Ĥ⟩ has the basis to decide halting. >> >> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ must use the same basis. >> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts >> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt >> >> Execution trace of Ĥ applied to ⟨Ĥ⟩ >> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H >> (b) Ĥ.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 >> *The same execution trace occurs even when the infinite loop is removed* >> >> Proves that Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ must abort its simulation and thus transition >> to Ĥ.Hqn. As long as Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ can somehow see this then H ⟨Ĥ⟩ ⟨Ĥ⟩ >> applies this same basis an transitions to H.qy >> >> *Criterion Measure* >> *Determine halt status from simulating halt deciders POV* >> H is assumed to be a simulating termination analyzer that aborts the >> simulation of any input that would cause its own non-termination and >> returns NO. Otherwise H always returns YES. > > If you don't want to explain your work, there is a less verbose way to > avoid explaining. > Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt Immediately determines that it is about to simulate itself with its own TMD by comparing its last param to its first two Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer