Re: Halting Problem Solved

Subject	Re: Halting Problem Solved
Newsgroups	comp.theory
References	(5 earlier) <scuq00$f3u$1@dont-email.me> <yqednYuPEb9_mm79nZ2dnUU7-N3NnZ2d@giganews.com> <sd0t3v$s8h$1@dont-email.me> <sd12d2$1hj5$1@gioia.aioe.org> <sd19i9$p9r$1@dont-email.me>
From	Richard Damon <Richard@Damon-Family.org>
Message-ID	<tdWII.36661$UR4.14315@fx37.iad> (permalink)
Organization	Forte - www.forteinc.com
Date	2021-07-18 07:42 -0600

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On 7/18/21 7:15 AM, David Brown wrote:
> On 18/07/2021 13:13, Andy Walker wrote:
>> On 18/07/2021 10:43, David Brown wrote:
>> ["You" == PO, of course]
>>> It would mean you have a claim (without proof - but we are assuming you
>>> are correct) that you can find an algorithm H that correctly tells if a
>>> given computation will halt or not, but only works for some functions.
>>> If you call H with input (P, X) which it likes, it will correctly give
>>> out yes or no.  If it doesn't like (P, X) - the input is "pathological",
>>> then it might say "yes", it might say "no", it might say "neither", it
>>> might never stop with an answer.
>>
>>     Well, /that/ claim is trivially true, eg if "H" replies "don't
>> know" to every instance presented to it.  There are also less trivial
>> "H"'s, eg one that emulates "P(X)", replies "yes" if the emulation halts,
>> "no" if it repeats exactly a previous state , and otherwise either just
>> keeps going or else gives up after some large number of steps.
>>
>>     AFAACT, given the amount of obfuscation around it, PO's
>> current emulator is broadly of this type.  It has though, of course,
>> nothing to do with the actual Halting Problem or related proofs.
>>
>>> Basically, it would be useless.
>>
>>     Although the sentiment is correct, your claim isn't.  There are
>> /useful/ programs that correctly reply "yes", correctly reply "no", or
>> halt and reply "sorry, can't tell".  [Proof checkers are of this general
>> nature.]  Basically, the third response is not [necessarily] caused by
>> pathology, but could be thought of as a plea for more information.  As
>> a debugging aid, "H" could point out the constructions that prevent it
>> from reaching a definite conclusion, such as uncounted loops without
>> [eg] corresponding invariants proving that the loop terminates.  This
>> serves as a hint to the programmer that [eg] an extra check is needed.
>> A lot of relevant analysis is already done by aggressive optimisation,
>> which is a closely-related area of program analysis.
>>
> 
> If the function could be relied upon to answer "sorry, can't tell" (or
> even reliably fail to halt) for inputs when it can't determine the
> correct answer, it would be useful.  But that's not how these partial
> deciders that Olcott and Mr. Flibble like actually work.  They say you
> are not allowed to give them "pathological" inputs - inputs that the
> function can't handle reliably.  They don't give any guarantees about
> the output with such inputs - their function might say "yes", or might
> say "no", or might say "I can't tell", or might not halt, or might
> launch nasal daemons.
> 
> This also means that if you give the function some input and it says
> "Yes, this will halt", it might be wrong - perhaps the input was
> "pathological" and the function is just making stuff up.
> 
> That's why I say it is useless.
> 

A function that sometimes responds 'I don't know' might be practically
useful, but I suspect isn't going to be useful for the Theoretical uses
that Turing Machines are designed for.

A function that is sometimes wrong might still be useful in some limited
cases. After all, we do use medical tests that sometimes give wrong
answers as long as we have an idea of the likelihood and maybe even the
sort of cases they get wrong. They can point us to maybe needing to use
a more extensive test. This is especially useful if they are only wrong
one way (or at least for a very large percent of the cases only wrong
one way).

Thread

Halting Problem Solved (Black Box Decider Theory) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 19:00 +0100
  Re: Halting Problem Solved (Black Box Decider Theory) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 19:28 +0100
    Re: Halting Problem Solved (Black Box Decider Theory) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 19:31 +0100
      Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 14:24 -0500
      Re: Halting Problem Solved (Black Box Decider Theory) Alan Mackenzie <acm@muc.de> - 2021-07-16 19:46 +0000
        Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 14:56 -0500
        Re: Halting Problem Solved (Black Box Decider Theory) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 20:56 +0100
          Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 15:00 -0500
            Re: Halting Problem Solved (Black Box Decider Theory) Alan Mackenzie <acm@muc.de> - 2021-07-16 22:42 +0000
          Re: Halting Problem Solved (Black Box Decider Theory) Alan Mackenzie <acm@muc.de> - 2021-07-16 22:24 +0000
            Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 17:32 -0500
              Re: Halting Problem Solved (Black Box Decider Theory) Alan Mackenzie <acm@muc.de> - 2021-07-16 22:54 +0000
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] olcott <NoOne@NoWhere.com> - 2021-07-16 23:15 -0500
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Alan Mackenzie <acm@muc.de> - 2021-07-17 09:10 +0000
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] olcott <NoOne@NoWhere.com> - 2021-07-17 09:37 -0500
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 17:24 +0100
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] olcott <NoOne@NoWhere.com> - 2021-07-17 12:06 -0500
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-18 02:45 +0100
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Mr Flibble <flibble@reddwarf.jmc> - 2021-07-18 12:26 +0100
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] olcott <NoOne@NoWhere.com> - 2021-07-19 09:41 -0500
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 01:36 +0100
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Alan Mackenzie <acm@muc.de> - 2021-07-17 17:11 +0000
                Re: Halting Problem Solved (Black Box Decider Theory)[ Strachey P ] Richard Damon <Richard@Damon-Family.org> - 2021-07-17 07:40 -0600
              Re: Halting Problem Solved (Black Box Decider Theory) David Brown <david.brown@hesbynett.no> - 2021-07-17 16:47 +0200
          Re: Halting Problem Solved (Black Box Decider Theory) David Brown <david.brown@hesbynett.no> - 2021-07-17 16:37 +0200
            Re: Halting Problem Solved (Black Box Decider Theory) [ Flibble is correct ] olcott <NoOne@NoWhere.com> - 2021-07-17 11:40 -0500
              Re: Halting Problem Solved (Black Box Decider Theory) [ Flibble is correct ] David Brown <david.brown@hesbynett.no> - 2021-07-18 11:43 +0200
                Re: Halting Problem Solved Andy Walker <anw@cuboid.co.uk> - 2021-07-18 12:13 +0100
                Re: Halting Problem Solved David Brown <david.brown@hesbynett.no> - 2021-07-18 15:15 +0200
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-18 07:42 -0600
                Re: Halting Problem Solved David Brown <david.brown@hesbynett.no> - 2021-07-18 17:02 +0200
                Re: Halting Problem Solved Jeff Barnett <jbb@notatt.com> - 2021-07-18 10:12 -0600
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-18 13:22 -0500
                Re: Halting Problem Solved Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-07-18 12:30 -0700
                Re: Halting Problem Solved [ Pathological self-reference error (Olcott 2004) ] olcott <NoOne@NoWhere.com> - 2021-07-19 08:41 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-18 19:55 -0700
                Re: Halting Problem Solved David Brown <david.brown@hesbynett.no> - 2021-07-18 21:00 +0200
                Re: Halting Problem Solved Jeff Barnett <jbb@notatt.com> - 2021-07-18 14:22 -0600
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-18 20:08 -0700
                Re: Halting Problem Solved Jeff Barnett <jbb@notatt.com> - 2021-07-19 02:06 -0600
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-19 21:09 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 11:24 +0100
                Re: Halting Problem Solved Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-20 03:43 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 13:53 +0100
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 14:02 +0100
                Re: Halting Problem Solved Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-20 06:30 -0700
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-20 10:22 -0700
                Re: Halting Problem Solved David Brown <david.brown@hesbynett.no> - 2021-07-19 09:11 +0200
                Re: Halting Problem Solved "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-19 01:13 -0700
                Re: Halting Problem Solved "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-19 11:34 -0700
                Re: Halting Problem Solved Jeff Barnett <jbb@notatt.com> - 2021-07-19 02:24 -0600
                Re: Halting Problem Solved David Brown <david.brown@hesbynett.no> - 2021-07-19 13:06 +0200
                Re: Halting Problem Solved Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-19 04:52 -0700
                Re: Halting Problem Solved Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-19 08:14 -0700
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-19 08:43 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-19 21:12 -0700
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-19 09:16 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-19 21:25 -0700
                Re: Halting Problem Solved Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-20 00:38 -0700
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-19 09:43 -0500
                Re: Halting Problem Solved (Black Box Decider Theory) [ Flibble is correct ] olcott <NoOne@NoWhere.com> - 2021-07-19 09:48 -0500
        Re: Halting Problem Solved (Black Box Decider Theory) Newberry <newberryxy@gmail.com> - 2021-07-19 13:30 -0700
          Re: Halting Problem Solved (Black Box Decider Theory) "dklei...@gmail.com" <dkleinecke@gmail.com> - 2021-07-20 16:16 -0700
            Re: Halting Problem Solved (Black Box Decider Theory) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 17:21 -0600
              Re: Halting Problem Solved (Black Box Decider Theory) "dklei...@gmail.com" <dkleinecke@gmail.com> - 2021-07-20 16:37 -0700
                Re: Halting Problem Solved (Black Box Decider Theory) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 18:37 -0600
                Re: Halting Problem Solved (Black Box Decider Theory) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 18:02 -0700
                Re: Halting Problem Solved (Black Box Decider Theory) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-20 23:32 -0700
                Re: Halting Problem Solved (Black Box Decider Theory) Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-07-21 08:17 -0700
                Re: Halting Problem Solved (Black Box Decider Theory) André G. Isaak <agisaak@gm.invalid> - 2021-07-21 09:24 -0600
            Re: Halting Problem Solved (Black Box Decider Theory) Newberry <newberryxy@gmail.com> - 2021-07-20 23:26 -0700
      Re: Halting Problem Solved (Black Box Decider Theory) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 21:57 +0100
        Re: Halting Problem Solved (Black Box Decider Theory) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 22:06 +0100
          Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 16:10 -0500
            Re: Halting Problem Solved (Black Box Decider Theory) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 22:22 +0100
              Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 16:30 -0500
  Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 13:31 -0500
    Re: Halting Problem Solved (Black Box Decider Theory) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 21:46 +0100
      Re: Halting Problem Solved (Black Box Decider Theory) olcott <NoOne@NoWhere.com> - 2021-07-16 16:07 -0500
        Re: Halting Problem Solved (Black Box Decider Theory) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 23:59 +0100
          Re: Halting Problem Solved [ Ben admits that he lied ] olcott <NoOne@NoWhere.com> - 2021-07-17 10:35 -0500
            Re: Halting Problem Solved [ Ben admits that he lied ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-18 03:32 +0100
              Re: Halting Problem Solved [ Ben admits that he lied ] olcott <NoOne@NoWhere.com> - 2021-07-19 09:55 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 01:35 +0100
                Re: Halting Problem Solved [ Ben admits that he lied ] olcott <NoOne@NoWhere.com> - 2021-07-20 09:22 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] André G. Isaak <agisaak@gm.invalid> - 2021-07-20 08:40 -0600
                Re: Halting Problem Solved [ Ben admits that he lied ] olcott <NoOne@NoWhere.com> - 2021-07-20 10:18 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] André G. Isaak <agisaak@gm.invalid> - 2021-07-20 09:29 -0600
                Re: Halting Problem Solved [ Ben admits that he lied ] Daniel Pehoushek <pehoushek1@gmail.com> - 2021-07-20 09:45 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] Richard Damon <Richard@Damon-Family.org> - 2021-07-20 10:33 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-21 01:28 +0100
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] olcott <NoOne@NoWhere.com> - 2021-07-21 09:48 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 09:41 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-22 01:12 +0100
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] olcott <NoOne@NoWhere.com> - 2021-07-21 20:27 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 18:37 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] olcott <NoOne@NoWhere.com> - 2021-07-21 20:49 -0500
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 19:01 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-22 02:49 +0100
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-21 20:57 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-21 19:19 -0700
                Re: Halting Problem Solved André G. Isaak <agisaak@gm.invalid> - 2021-07-21 20:57 -0600
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-21 22:25 -0500
                Re: Halting Problem Solved André G. Isaak <agisaak@gm.invalid> - 2021-07-21 21:50 -0600
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-21 23:40 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-21 22:26 -0700
                Re: Halting Problem Solved André G. Isaak <agisaak@gm.invalid> - 2021-07-22 00:55 -0600
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-22 08:04 -0500
                Re: Halting Problem Solved André G. Isaak <agisaak@gm.invalid> - 2021-07-22 08:23 -0600
                Re: Halting Problem Solved (title is a misnomer) olcott <NoOne@NoWhere.com> - 2021-07-22 09:52 -0500
                Re: Halting Problem Solved (title is a misnomer) Richard Damon <Richard@Damon-Family.org> - 2021-07-22 10:24 -0700
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-22 10:22 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-22 21:53 +0100
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-22 16:47 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-22 14:54 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-23 00:04 +0100
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-22 18:22 -0500
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-23 00:53 +0100
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-23 09:04 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-23 09:41 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-23 22:13 +0100
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-23 16:54 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-23 15:19 -0700
                Re: Halting Problem Solved Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-25 04:02 +0100
                Re: Halting Problem Solved André G. Isaak <agisaak@gm.invalid> - 2021-07-22 18:05 -0600
                Re: Halting Problem Solved olcott <NoOne@NoWhere.com> - 2021-07-23 08:36 -0500
                Re: Halting Problem Solved Richard Damon <Richard@Damon-Family.org> - 2021-07-23 08:51 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] [ H(P,P)==0 is correct ] "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-21 21:04 -0700
                Re: Halting Problem Solved [ Ben admits that he lied ] Richard Damon <Richard@Damon-Family.org> - 2021-07-19 21:17 -0700
        Re: Halting Problem Solved (Black Box Decider Theory) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 23:59 +0100
          Re: Halting Problem Solved (Black Box Decider Theory) [Ben is a liar ] olcott <NoOne@NoWhere.com> - 2021-07-17 10:38 -0500
            Re: Halting Problem Solved (Black Box Decider Theory) [Ben is a liar ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-18 03:12 +0100
              Re: Halting Problem Solved (Black Box Decider Theory) [Ben is a liar ] olcott <NoOne@NoWhere.com> - 2021-07-19 10:02 -0500
                Re: Halting Problem Solved (Black Box Decider Theory) [Ben is a liar ] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 01:36 +0100
  Re: Halting Problem Solved (Black Box Decider Theory) Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:12 -0700

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