XPost: comp.theory, sci.logic, sci.math   
   From: news.dead.person.stones@darjeeling.plus.com   
      
   On 19/11/2025 23:04, Jeff Barnett wrote:   
   > On 11/19/2025 12:42 PM, Mike Terry wrote:   
   >> On 19/11/2025 18:26, dart200 wrote:   
   >>> On 11/18/25 3:47 PM, Mike Terry wrote:   
   >>>> On 18/11/2025 03:10, dart200 wrote:   
   >>>>> On 11/17/25 7:07 PM, Kaz Kylheku wrote:   
   >>>>>> On 2025-11-18, dart200  wrote:   
   >>>>>>> On 11/17/25 4:31 PM, olcott wrote:   
   >>>>>>>> On 11/17/2025 6:06 PM, dart200 wrote:   
   >>>>>>>>> On 11/17/25 3:35 PM, olcott wrote:   
   >>>>>>>>>> The halting problem is requiring deciders to   
   >>>>>>>>>> compute information that is not contained in   
   >>>>>>>>>> their input.   
   >>>>>>>>>   
   >>>>>>>>> ur agreeing with turing and the halting problem:   
   >>>>>>>>>   
   >>>>>>>>> one cannot compute whether a machine halts or not from the string   
   >>>>>>>>> describing the machine   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> That the halting problem limits computation   
   >>>>>>>> is like this very extreme example:   
   >>>>>>>>   
   >>>>>>>> Predict who the next president of the United States   
   >>>>>>>> will be entirely on the basis of √2 (square root of 2).   
   >>>>>>>> That cannot be derived from the input.   
   >>>>>>>   
   >>>>>>> bruh, ur agreeing with the halting problem:   
   >>>>>>>   
   >>>>>>> one cannot take the string describing the machine, and use it to   
   compute   
   >>>>>>> whether the machine described halts   
   >>>>>>   
   >>>>>> But that isn't true; you certainly can do that. Just not using one   
   >>>>>> unified algorithm that works for absolutely all such strings.   
   >>>>>>   
   >>>>>> When it /does/ work, it's certainly not based on any input other than   
   >>>>>> the string.   
   >>>>>   
   >>>>> yes i meant generally   
   >>>>>   
   >>>>> you also can't compute generally whether you can or cannot compute   
   whether a an machine   
   >>>>> description halts or not   
   >>>>   
   >>>> What does that mean though?   
   >>>>   
   >>>> It sounds like you're asking for a /single/ TM that given /any/ machine   
   description D, must   
   >>>> compute "whether or not D's halting is computable". [And saying no such   
   single TM exists?]   
   >>>   
   >>> yes, it takes /single/ machine input a outputs whether /any/ other machine   
   could compute the   
   >>> input machine's halting semantics.   
   >>   
   >> Have you read Kaz's response to my post?  That explains why for any given   
   machine, there is always   
   >> some other machine that computes the halting status of that machine.    
   Basically there are only two   
   >> possible behaviours: halts or neverhalts.  We just need two machines H1   
   and H0 that straight away   
   >> return halts/neverhalts respectively.  For any machine M, either H1 or H0   
   correctly computes M's   
   >> halting status, so assuming normal terminology use, any single M is   
   decideable.  (And by   
   >> extension, halting for any finite set of machines is decidable.)   
   >>   
   >> Sometimes people attempt to come up with reasons why H1 and H0 don't   
   count.  That was certainly   
   >> PO's response, and his explanation was that H1 and H0 are disqualified as   
   halt deciders because   
   >> they "aren't even trying".  He has never explained what it means for a TM   
   to "not really try" to   
   >> do something; of course, TMs are just what they are, without "trying" to do   
   anything.  We're not   
   >> talking about an olympic sport where there are points awarded for   
   effort/artistic interpretation   
   >> etc., it's all just "whether they work".   
   >   
   > They don't count as *deciders* plain and simple because a *decider* must   
   decide correctly on all   
   > possible inputs.   
      
   A decider "for a single machine" is by definition a decider for the input   
   domain consisting of that   
   single machine-description.  Behaviour for other inputs is simply irrelevent.   
      
   If you want to consider a decider whose domain consists of all input strings,   
   then:   
   a)  obviously such a machine cannot be a halt decider.  The Linz proof shows   
   this.   
   b)  if we want a partial decider (as you describe below), then since a single   
        TM-description is effectively recognisable, we could replace my H1/H0   
   above   
        with adjusted versions H1'/H2' that first check whether their input is   
        a description of the M in question.  If not they return dontknow,   
   otherwise   
        they return halts/neverhalts as T1/T0 respectively.   
      
   But this is a separate question - we are actually considering an input domain   
   of one element.   
      
   > Even a partial decider must, for all possible inputs, return "yes", "no", or   
   "don't   
   > know" and must be correct when returning one of the first two. So that any   
   machine that returns the   
   > same value for all inputs, is a decider in a domain where the onto range   
   contains one and only one   
   > value, e.g., a halt decider that decides halting status for all possible   
   non-halting (TM, data)   
   > input - not very interesting.   
      
   Or a domain with just one element {M_desc}   
      
   > Neither is the example of a decider that returns "don't know" for all   
   > inputs. (Just to state the obvious: when something is said to return a value   
   halting of that   
   > something is entailed.)   
      
   No, Sorry but that's Just Wrong too.  Returning "don't know" for all input is   
   valid, but not very   
   interesting I admit.  PO has also said what you just said!  (Not that that   
   means it's automatically   
   wrong, but it's not a good sign! :)  Anyhow, my H1'/H0' above do not return   
   "don't know" for all   
   inputs.)   
      
      
   Mike.   
      
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