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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 13:22 +0000
Organization muc.de e.V.
Message-ID <sculjg$1q6c$6@news.muc.de> (permalink)
References <20210717135003.00000fdc@reddwarf.jmc>

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Mr Flibble <flibble@reddwarf.jmc> wrote:
> If it is impossible for a decider to be referenced by a pathological
> program for the purposes of defeating the decider (see Strachey [1965])
> then the all currently extant proofs which rely on the Strachey
> contradiction become invalid.

There is no such thing as a "pathological program" in this sense.  Every
program either terminates or does not terminate.

The only thing you could designate as "pathological" would be the
relationship between the program and your black box, not the program
itself.

> I have a theoretical design for such a decider which I am calling a
> black box decider as its internal mechanism of operation is unknown to
> that which is being decided; this does rely on simulating the candidate
> (program + input) which means the decision will be returned in FINITE
> time (even if this time exceeds the age of the universe in duration)
> rather than being UNDECIDABLE.

The black-box approach won't help you.  The theorem rules out a
_universal_ halt decider, that means a decider which decides _any_
program.  There will be programs which confound your black box, despite
your attempts to make it difficult to construct these - they still
exist.  And for those programs, your black box will return the wrong
result.

> Method:

> 1) A trusted operator creates a digital signature, S, by digitally
> signing the candidate program, P and its input, I.
> 2) Operator runs the black box decider, D, passing it P, I, and
> and S.
> 3) If S is invalid (i.e. isn't signed by a trusted operator) D will
> abort due to P being pathological (i.e. it is attempting to defeat D by
> referencing D).
> 4) If the candidate digital signature is valid the decider simulates
> the P+I to determine if P halts or not (how long this takes
> depends on the complexity of the simulator and the candidate so this may
> take a very long (but FINITE) time).

> D will then return one of THREE results to the operator:

> a) P halts;
> b) P does not halt;
> c) P is invalid (attempted to defeat the decider).

So, D isn't a halt decider, because there are programs for which it
fails to return the correct yes/no result.  Note, again, that in case
c), there is nothing invalid about the program itself; it will run and
either halt or not halt.  It is the relationship between P and D that
you are calling "invalid".  I would go further and say that it is D
which is invalid, since it cannot perform its purported function.

> Obviously this solution depends on the strength of the digital
> signature encryption being such that breaking it would exceed the
> time used to reach a decision for P.

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.

> Halting Problem solved? Debatable.

Not really.  You should really get into a proof of the halting problem
theorem and _understand_ it.

> Currently extant proofs valid? Not so much.

These proofs remain totally valid.  Since they do not depend on the
internal workings of the purported decider, no amount of cleverness and
deviousness in this area is going to make the slightest difference.
This is what is so baffling Olcott, due to his inability to understand
the concept of a proof.

You are a computer science graduate, right?  Surely, unlike Olcott, you
do understand the concept of a proof, and that the halting problem
theorem is proven?

> /Flibble

-- 
Alan Mackenzie (Nuremberg, Germany).

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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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