Re: Halting Problem Solved? (Black Box Decider Theory) V2

From	Alan Mackenzie <acm@muc.de>
Newsgroups	comp.theory
Subject	Re: Halting Problem Solved? (Black Box Decider Theory) V2
Date	2021-07-17 14:34 +0000
Organization	muc.de e.V.
Message-ID	<scupqd$1q6c$9@news.muc.de> (permalink)
References	(2 earlier) <20210717143722.00007f34@reddwarf.jmc> <scunn6$1q6c$7@news.muc.de> <20210717150602.00003bc6@reddwarf.jmc> <scuovq$1q6c$8@news.muc.de> <20210717152448.00006958@reddwarf.jmc>

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Mr Flibble <flibble@reddwarf.jmc> wrote:
> On Sat, 17 Jul 2021 14:20:42 -0000 (UTC)
> Alan Mackenzie <acm@muc.de> wrote:

>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>> > On Sat, 17 Jul 2021 13:59:02 -0000 (UTC)
>> > Alan Mackenzie <acm@muc.de> wrote:  

>> >> Mr Flibble <flibble@reddwarf.jmc> wrote:  
>> >> > On Sat, 17 Jul 2021 13:22:56 -0000 (UTC)
>> >> > Alan Mackenzie <acm@muc.de> wrote:    
>> >> >> Not really - you don't have a universal halting decider here by
>> >> >> design. And even if you did, the signature wouldn't do anything
>> >> >> to prevent the existence of the programs which have an "invalid
>> >> >> relationship" with D.    

>> >> > The point is that this "invalid relationship" is DETECTABLE by
>> >> > the black box decider.    

>> >> I think, but I'm not sure, that such relationships cannot be
>> >> detected, that it's another one of these limitation theorems.  Ben
>> >> could probably say more on this.  

>> >> > This "invalid relationship" only exists for programs which are
>> >> > deliberately designed to defeat the decider ....    

>> >> Not at all.  There will be random programs, not deliberately
>> >> designed, which will also have such a relationship with the
>> >> purported decider.  

>> >> > .... which are uninteresting cases because presumably we are
>> >> > using a decider to decide legitimate programs that have serve
>> >> > some useful purpose beyond the HP itself.    

>> >> Then you're not talking about the standard halting problem.  That
>> >> shows the impossibility of a decider which can decide ANY program.
>> >> If you limit the scope of the programs handled, then you might well
>> >> construct a practically useful partial decider.  Difficult, but
>> >> possible.  There are probably theorems about the sort of things
>> >> that are possible here, but I don't know them.  

>> >> None of this has any relevance for the theoremhood of the halting
>> >> problem result itself.  

>> > Disagree: having a third result for invalid pathological programs
>> > whilst novel is still a result, i.e. a decision reached in finite
>> > time.  

>> Let me stress again that there is nothing invalid or pathological
>> about these programs, and they can run and halt or not halt like any
>> other program.  It is only in their relationship with H where they
>> are special, in that H is unable to determine their halting status
>> correctly.

>> That's assuming it's possible for H to single out such programs.  I
>> don't know if this is possible in the general case, but I suspect
>> it's not. Again, Ben or Richard might know more about this.

>> But all this is moving away from the halting problem.

> Disagree: as the decider is a black box if it can always detect when it
> is being invoked, either directly by the trusted operator or indirectly
> by P which does not have the trusted operator's private key in order to
> digitally sign P and I that is passed to the decider.

P might contain a copy of D's algorithm (with or without the key stuff),
and indeed P might contain a copy of the private key.  Such programs
_exist_, whether or not we could as humans create them.  As I say, I
don't think it's possible for D to detect an algorithm which does the
same as D.

But in any case, D is not behaving as a universal halting detector, in
that it doesn't return halts/doesn't halt for all input programs.

> /Flibble

-- 
Alan Mackenzie (Nuremberg, Germany).

Thread

Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 13:50 +0100
  Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 13:22 +0000
    Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 14:37 +0100
      Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 13:59 +0000
        Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:06 +0100
          Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 09:17 -0500
          Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 14:20 +0000
            Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:24 +0100
              Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 14:34 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:38 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 14:45 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:53 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 15:12 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) [ Rice's Theorem ] olcott <NoOne@NoWhere.com> - 2021-07-17 11:53 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 20:38 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 wij <wyniijj@gmail.com> - 2021-07-17 08:04 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 16:12 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 wij <wyniijj@gmail.com> - 2021-07-17 08:25 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 16:28 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 wij <wyniijj@gmail.com> - 2021-07-17 08:37 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 11:58 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-17 14:17 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 11:23 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 17:45 +0100
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 12:08 -0500
            Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 11:17 -0500
              Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 20:05 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 15:19 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-17 20:51 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 16:48 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-18 10:57 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Richard Damon <Richard@Damon-Family.org> - 2021-07-18 07:36 -0600
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-19 08:58 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Richard Damon <Richard@Damon-Family.org> - 2021-07-19 08:23 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-19 18:20 +0000
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-20 08:25 -0500
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Alan Mackenzie <acm@muc.de> - 2021-07-20 17:35 +0000
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 13:26 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Alan Mackenzie <acm@muc.de> - 2021-07-20 18:53 +0000
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 14:04 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 12:27 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 13:49 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 17:14 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 16:27 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 18:20 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 18:34 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 21:04 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 20:24 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 22:06 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 20:21 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 21:26 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 22:53 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 22:02 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) olcott <NoOne@NoWhere.com> - 2021-07-20 23:24 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 22:12 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) André G. Isaak <agisaak@gm.invalid> - 2021-07-20 23:32 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ DOES NOT HOLD ] olcott <NoOne@NoWhere.com> - 2021-07-21 09:11 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ DOES NOT HOLD ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 10:03 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ DOES NOT HOLD ] olcott <NoOne@NoWhere.com> - 2021-07-21 11:11 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ DOES NOT HOLD ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 10:42 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ DOES NOT HOLD ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 10:16 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 21:23 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 11:45 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 10:22 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] olcott <NoOne@NoWhere.com> - 2021-07-21 12:23 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 10:41 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 12:26 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] olcott <NoOne@NoWhere.com> - 2021-07-21 13:54 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 13:26 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] olcott <NoOne@NoWhere.com> - 2021-07-21 14:44 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 12:56 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 15:09 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] olcott <NoOne@NoWhere.com> - 2021-07-21 16:29 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 15:02 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-21 21:08 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ global halt decider ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 12:55 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 11:29 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 12:51 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 12:19 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 13:49 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 13:22 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 14:43 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 13:12 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ][ADD] olcott <NoOne@NoWhere.com> - 2021-07-21 16:07 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ][ADD] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 14:32 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ][ADD] olcott <NoOne@NoWhere.com> - 2021-07-21 16:50 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ][ADD] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 15:07 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 15:06 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 16:22 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 14:38 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 15:57 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 17:21 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 15:53 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] André G. Isaak <agisaak@gm.invalid> - 2021-07-21 16:59 -0600
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 20:21 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 18:53 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 13:07 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] olcott <NoOne@NoWhere.com> - 2021-07-21 15:29 -0500
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) [ Paradox rather than contradiction ] Richard Damon <Richard@Damon-Family.org> - 2021-07-21 14:08 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 19:33 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 18:07 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 12:14 -0700
                Re: Halting Problem Solved? ( H(P,P)==0 is correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-20 12:06 -0700
                Re: Halting Problem Solved? (Black Box Decider Theory) V2 Richard Damon <Richard@Damon-Family.org> - 2021-07-20 10:39 -0700
          Re: Halting Problem Solved? (Black Box Decider Theory) V2 Andy Walker <anw@cuboid.co.uk> - 2021-07-17 15:55 +0100
      Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 09:18 -0500
        Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:20 +0100
          Re: Halting Problem Solved? (Black Box Decider Theory) V2 olcott <NoOne@NoWhere.com> - 2021-07-17 11:13 -0500
  Re: Halting Problem Solved? (Black Box Decider Theory) V2 wij <wyniijj@gmail.com> - 2021-07-17 06:57 -0700
    Re: Halting Problem Solved? (Black Box Decider Theory) V2 Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 15:17 +0100
      Re: Halting Problem Solved? (Black Box Decider Theory) V2 wij <wyniijj@gmail.com> - 2021-07-17 07:36 -0700

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