Path: ...!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_A_simulating_halt_decider_applied_to_the_The_Peter_?= =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?= Date: Thu, 30 May 2024 08:20:09 -0500 Organization: A noiseless patient Spider Lines: 134 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 30 May 2024 15:20:10 +0200 (CEST) Injection-Info: dont-email.me; posting-host="0a722b73a14c6c7bef786c05822a9348"; logging-data="1799593"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19ZfcWCtAvwisSYA7wg5Pra" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:MX/zOBWb9UaRKbB6PfVzDRHrLaY= Content-Language: en-US In-Reply-To: Bytes: 7154 On 5/30/2024 2:06 AM, Mikko wrote: > On 2024-05-29 13:13:13 +0000, olcott said: > >> On 5/29/2024 3:37 AM, Mikko wrote: >>> On 2024-05-28 11:34:24 +0000, Richard Damon said: >>> >>>> On 5/27/24 10:59 PM, olcott wrote: >>>>> On 5/27/2024 9:52 PM, Richard Damon wrote: >>>>>> On 5/27/24 10:41 PM, olcott wrote: >>>>>>> On 5/27/2024 9:23 PM, Richard Damon wrote: >>>>>>>> On 5/27/24 10:01 PM, olcott wrote: >>>>>>>>> On 5/27/2024 8:24 PM, Richard Damon wrote: >>>>>>>>>> On 5/27/24 9:04 PM, olcott wrote: >>>>>>>>> >>>>>>>>>>>>> I totally do. Can you please write down the >>>>>>>>>>>>> "completely specified state transition/tape operation table." >>>>>>>>>>>>> of this specific (thus uniquely identifiable) machine I would >>>>>>>>>>>>> really like to see it. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> But it was proven that no such machine exists! >>>>>>>>>>>> >>>>>>>>>>>> Remember, the proof starts with the hypothetical that such a >>>>>>>>>>>> machine exists. Such a machine WOULD HAVE a completely >>>>>>>>>>>> specified state transition/tape operation table. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> That is not what you said. >>>>>>>>>>>  >>>>> There doesn't need to be a unique finite string, but >>>>>>>>>>> it is a 100% >>>>>>>>>>>  >>>>> completely specified state transition/tape operation >>>>>>>>>>> table. >>>>>>>>>>> >>>>>>>>>>> "a 100% completely specified state transition/tape operation >>>>>>>>>>> table" >>>>>>>>>>> of a non-existent machine. >>>>>>>>>> >>>>>>>>>> Right, by presuming that you have a Turing Machine, you have a >>>>>>>>>> completly specified state transition/tape operation table. >>>>>>>>>> >>>>>>>>>> You may not KNOW what that table is if you don't know what the >>>>>>>>>> exact machine is, but you know it exists. >>>>>>>>> >>>>>>>>>  >>> But it was proven that no such machine exists! >>>>>>>>>  > ... but you know it exists. >>>>>>>>> >>>>>>>>>  >>> But it was proven that no such machine exists! >>>>>>>>>  > ... but you know it exists. >>>>>>>>> >>>>>>>>>  >>> But it was proven that no such machine exists! >>>>>>>>>  > ... but you know it exists. >>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Really, then show that one exists! >>>>>>>> >>>>>>> >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> *I am quoting your words. You did contradict yourself* >>>>>>> >>>>>> >>>>>> >>>>>> Really, where did I say that H exists? >>>>>> >>>>>> I said that if a Turing Machine exists, then its transition table >>>>>> does too. >>>>>> >>>>> >>>>> OK my mistake this time. I did not take into account the full context. >>>>> I will go back an read the Linz proof and see if he said anything >>>>> about a specific machine. >>>> >>>> Read the DEFINITION of the problem. He talks about "a" machine. >>>> Using a singular article means you are working with just one. >>>> >>>> >>>> Taking stuff out of context is a common problem with you, when you >>>> don't understand something, you just make up what it must mean, and >>>> stick to that. That isn't the way to learn. >>>> >>>> >>>>> >>>>> None of the proofs ever try to show that there exists one machine that >>>>> gets the wrong answer. They are always at least trying to prove >>>>> that no >>>>> machine of the infinite set of machine gets the right answer. >>>>> >>>> >>>> What I see, is they always start with a prototypical single machine, >>>> and show that it gets the answer wrong, and then they use >>>> categorical logic to say that we can do this same thing for all of >>>> them. >>> >>> It is possible to formulate the claim and proof so that H is an >>> universally >>> quantified variable. But the usual way is apparently equally good for >>> the >>> target audience. >>> >> >> *Formalizing the Linz Proof structure* >> ∃H  ∈ Turing_Machines >> ∀x  ∈ Turing_Machines_Descriptions >> ∀y  ∈ Finite_Strings >> such that H(x,y) = Halts(x,y) > > That is not a proof structure. That is the counter-hypothesis of Linz' > proof. > Also note that both x and y are finite strings. > The above is what Linz is claiming evaluates to false, he says there is no such H. A decider computes the mapping from finite string inputs to its own accept or reject state. A decider does not and cannot compute the mapping from Turing_Machine inputs to its own accept or reject state. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer