Path: ...!news.nobody.at!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: =?utf-8?Q?Re:_A_simulating_halt_decider_applied_to_the_The_Peter_Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?= Date: Fri, 31 May 2024 16:00:44 +0300 Organization: - Lines: 131 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 31 May 2024 15:00:45 +0200 (CEST) Injection-Info: dont-email.me; posting-host="712b1ae307b3aa2da9924d76e81b0b6d"; logging-data="2359744"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/z1Hh4Peec0suHNHCX86zp" User-Agent: Unison/2.2 Cancel-Lock: sha1:q8EYBmrH53cSSruSG1Q5ix+Kx5c= Bytes: 7066 On 2024-05-30 13:20:09 +0000, olcott said: > 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. Yes, and proves the claim. > A decider computes the mapping from finite string inputs to > its own accept or reject state. An existing decider. > A decider does not and cannot compute the mapping from Turing_Machine > inputs to its own accept or reject state. An exsiting decider. -- Mikko