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| From | dart200 <user7160@newsgrouper.org.invalid> |
|---|---|
| Newsgroups | comp.theory, sci.logic, sci.math, comp.ai.philosophy |
| Subject | Re: a subset of Turing machines can still be Turing complete PLO |
| Date | 2026-01-25 13:07 -0800 |
| Organization | A noiseless patient Spider |
| Message-ID | <10l60mn$1s352$4@dont-email.me> (permalink) |
| References | (11 earlier) <af7dR.591258$VY9.160696@fx10.iad> <10l3h2c$11a9n$10@dont-email.me> <kPddR.598537$VY9.364398@fx10.iad> <10l416g$1a2so$4@dont-email.me> <q9tdR.98058$4e1.25226@fx20.iad> |
Cross-posted to 4 groups.
On 1/25/26 10:20 AM, Richard Damon wrote: > On 1/24/26 10:03 PM, dart200 wrote: >> On 1/24/26 4:52 PM, Richard Damon wrote: >>> On 1/24/26 5:28 PM, dart200 wrote: >>>> On 1/24/26 9:24 AM, Richard Damon wrote: >>>>> On 1/24/26 11:49 AM, dart200 wrote: >>>>>> On 1/24/26 4:24 AM, Richard Damon wrote: >>>>>>> On 1/24/26 4:21 AM, dart200 wrote: >>>>>>>> On 1/24/26 12:42 AM, Mikko wrote: >>>>>>>>> On 23/01/2026 07:21, dart200 wrote: >>>>>>>>>> On 1/22/26 3:58 PM, olcott wrote: >>>>>>>>>>> It is self-evident that a subset of Turing machines >>>>>>>>>>> can be Turing complete entirely on the basis of the >>>>>>>>>>> meaning of the words. >>>>>>>>>>> >>>>>>>>>>> Every machine that performs the same set of >>>>>>>>>>> finite string transformations on the same inputs >>>>>>>>>>> and produces the same finite string outputs from >>>>>>>>>>> these inputs is equivalent by definition and thus >>>>>>>>>>> redundant in the set of Turing complete computations. >>>>>>>>>>> >>>>>>>>>>> Can we change the subject now? >>>>>>>>>> >>>>>>>>>> no because perhaps isolating out non-paradoxical machine may >>>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>>> paradoxes, removing a core pillar in the undecidability >>>>>>>>>> arguments. >>>>>>>>> >>>>>>>>> The set of non-paradoxical Turing machines is indeed Truing >>>>>>>>> complete >>>>>>>>> because there are no paradoxical Turing machines. Of course any >>>>>>>>> Turing >>>>>>>>> machine can be mentioned in a paradox. >>>>>>>>> >>>>>>>> >>>>>>>> i don't see how the lack of paradoxes ensures all possible >>>>>>>> computations are represented (therefore being turing complete). >>>>>>> >>>>>>> In other words, you disagree with you own claim. >>>>>> >>>>>> may argument is that paradoxes are redundant, mikko did not add >>>>>> such a claim. so ur suggesting he was agreeing with my rational >>>>>> that they are redundant? >>>>> >>>>> "Redundent" isn't really defined in Computation Theory. >>>> >>>> that's because i'm exploring it in ways that previous have gone >>>> unexplored >>>> >>>>> >>>>> ALL machines that compute the same answers are considered to be >>>>> semantically equivalent. >>>> >>>> and anything more than the first one which produces a particular >>>> result is redundant in terms of a minimal turing complete subset of >>>> machines. >>>> >>>>> >>>>> Part of your problem is you don't understand that trying to base >>>>> you idea on an uncomputable filter won't help you. >>>> >>>> from the reference point of a partial recognizer for functional >>>> equivalence, two machines can be one of three semantic classifications: >>>> >>>> - decidable non-equivalent >>>> - decidable equivalent >>>> - undecidable >>>> >>>> since a partial recognizer only has two output: true/false, we merge >>>> one of the decidable results with undecidable for the false output, >>>> and we are left with a partial recognizer for the other decidable >>>> result >>>> >>> >>> And "Partial Recognizers" are well known and nothing new, >> >> i suppose it's progress that we've gone from u repeatedly calling them >> "liars" because they merge results, to "well known and nothing new"... >> 🫩🫩🫩 > > Well, people calling the "Deciders" and ignoring the partial are liars. > > >> >>> >>>> there's no way to produce a contradiction with such a machine. from >>>> the reference of any given classifier an input can either be >>>> decidedly decidable or not decidable. if it's decidedly decidable >>>> the we can output the classification, if it's not decidable then we >>>> cannot. there's no middle ground here to exploit for a contradiction >>> >>> And the "contradiction" input just makes sure that its recognizer >>> can't decide on it, making sure it is just a partial recognizer. >>> >>>> >>>> as we iterate down the full enumeration of machines to build a >>>> minimal turing complete subset, we can test each one for functional >>>> non- equivalence against all previous found to be in that subset, >>>> with a non- equivalence partial recognizer that outputs true iff >>>> decidedly non- equivalent, or false iff decidedly equivalent OR not >>>> decidable. only if a machine returns true when tested against all >>>> previous machines in the subset is it then added to the minimal >>>> turing complete subset. both machines with any decidable equivalence >>>> or undecidability with respect to machines already in the subset are >>>> therefore not put in the subset >>> >>> And what good is this set. You don't know if it is even Turing >>> Complete Set (which it likely isn't). >> >> if it can be proven that no paradoxical machine is the simplest of all >> machines functionally equivalent to that paradoxical machine ... >> >> then just excluding paradoxical machines does not reduce the >> completeness of the minimal turing complete subset. >> >> yes i get that i haven't proven that to u 🙄🙄🙄 > > The problem is the results of the "paradoxical" machine was never the > problem, it was that the decider gave the wrong answer to it. > > You seem to think there is something problematical about these > "paradoxical" machines in general. philosophical errors are inherently limiting in ways we can't even truly imagine, so why bother trying to explain fully? > > It is just that it make one particular machine wrong, and that one > exists for every decider. if my thesis is correct: a minimal turing complete subset of turing machines cannot be shown to have a halting problem, removing a core pillar of undecidability proofs. i get that u have basically no creativity or wonder left in ur soul, but that potential excites me with the theoretical progress it might induce. > > >> >>> >>> >>>> >>>>> >>>>>> >>>>>>> >>>>>>>> >>>>>>>> paradoxical machines are still produce computations ... just not >>>>>>>> computations that are unique in their functional result compared >>>>>>>> to non- paradoxical ones. >>>>>>>> >>>>>>> >>>>>>> The problem is no machine is generically a "paradox". In the >>>>>>> proof, it is only a paradox to a particular machine that it refutes. >>>>>>> >>>>>>> The construction template (which isn't a machine, but a formula >>>>>>> to build a machine) is paradoxical to the Halt Decider API (which >>>>>>> again isn't a machine but a definition of the mapping for a >>>>>>> machine to generate). >>>>>>> >>>>>>> You (like Peter) just confuse classes of machines with machines >>>>>>> themselves, which is just an error. >>>>>> >>>>>> any machine in that class is a paradox >>>>>> >>>>> >>>>> Then you consider truth to be a paradox, and paradox to be an >>>>> uncomputeable property. >>>> >>>> no idea why u said that >>>> >>> >>> Because the machine you just tried to classify, are really no >>> different if form than others you don't do so. Your criteria is based >>> on uncomputable values. >> >> i apologize, that did not clarify anything to me >> > > You are trying to make a class of machines that can't actually be > computationally determined. > > Looking at just the machine, there is nothing in it that says "I am a > paradoxical machine", you first need to determine that it is using a > sub-machine in a contrary manner, which means you need to be able to > recognize that a machine is an attempt to be a halt decider. if my thesis is correct: that paradoxical machines *never* form the simplest machine of their class of functionally equivalent machines, then any machine that involves a paradox will be necessarily excluded from a minimal turing complete subset simply due to the natural increase in complexity it takes to describe the semantic structures of a paradox over non-paradoxical functionally-equivalent machiens ... the only paradox we need to consider handling is that in-regards to the functional-equivalence partial-recognizor we're dealing, but i've already explained how it's handled: any machine that does not test as true (decidable non-equivalent) for /all/ machines previously found in the subset is excluded (which will also exclude possible paradoxes that can fail the equivalence test for not being decidable) -- arising us out of the computing dark ages, please excuse my pseudo-pyscript, ~ nick
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a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-20 19:06 -0800
Re: a subset of turing machines can still be turing complete Richard Damon <Richard@Damon-Family.org> - 2026-01-20 22:43 -0500
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-21 08:38 -0800
Re: a subset of turing machines can still be turing complete Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-22 01:05 +0000
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-22 15:21 -0800
Re: a subset of turing machines can still be turing complete Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-22 23:56 +0000
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-22 21:51 -0800
Re: a subset of turing machines can still be turing complete Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-23 11:53 -0500
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-23 10:30 -0800
Re: a subset of turing machines can still be turing complete Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-23 17:59 -0500
Re: a subset of turing machines can still be turing complete Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-28 23:22 +0000
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-29 21:18 -0800
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-22 17:58 -0600
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-22 21:21 -0800
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 04:19 -0600
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-23 08:29 -0800
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 11:14 -0600
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 11:24 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-23 18:01 -0500
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 17:50 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-23 20:30 -0500
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 19:51 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-23 20:56 -0500
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-23 21:05 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 07:16 -0500
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-24 08:21 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-24 09:39 -0500
Re: a subset of Turing machines can still be Turing complete PLO olcott <polcott333@gmail.com> - 2026-01-24 09:48 -0600
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 12:19 -0500
Re: a subset of Turing machines can still be Turing complete PLO Mikko <mikko.levanto@iki.fi> - 2026-01-24 10:42 +0200
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 01:21 -0800
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 07:24 -0500
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 08:49 -0800
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 12:24 -0500
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 14:28 -0800
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 19:52 -0500
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 19:03 -0800
Re: a subset of Turing machines can still be Turing complete PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:20 -0500
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-25 13:07 -0800
Re: a subset of Turing machines can still be Turing complete PLO Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-29 00:15 +0000
Re: a subset of Turing machines can still be Turing complete PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-29 00:28 -0800
Re: a subset of Turing machines can still be Turing complete PLO Mikko <mikko.levanto@iki.fi> - 2026-01-25 13:12 +0200
Re: a subset of turing machines can still be turing complete Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 22:41 -0500
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-22 21:44 -0800
Re: a subset of turing machines can still be turing complete Richard Damon <Richard@Damon-Family.org> - 2026-01-23 11:59 -0500
Re: a subset of turing machines can still be turing complete dart200 <user7160@newsgrouper.org.invalid> - 2026-01-23 10:42 -0800
Re: a subset of turing machines can still be turing complete Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-23 17:45 -0500
Re: a subset of turing machines can still be turing complete Mikko <mikko.levanto@iki.fi> - 2026-01-21 10:45 +0200
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