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Re: Halting Problem Solved

From David Brown <david.brown@hesbynett.no>
Newsgroups comp.theory
Subject Re: Halting Problem Solved
Date 2021-07-19 09:11 +0200
Organization A noiseless patient Spider
Message-ID <sd38ib$hl$1@dont-email.me> (permalink)
References (10 earlier) <tdWII.36661$UR4.14315@fx37.iad> <sd1fr4$9f8$1@dont-email.me> <sd1jt8$sta$1@dont-email.me> <sd1toi$ocl$1@dont-email.me> <sd22hg$j6u$1@dont-email.me>

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On 18/07/2021 22:22, Jeff Barnett wrote:
> On 7/18/2021 1:00 PM, David Brown wrote:
>> On 18/07/2021 18:12, Jeff Barnett wrote:
>>> On 7/18/2021 9:02 AM, David Brown wrote:
>>>> On 18/07/2021 15:42, Richard Damon wrote:
>>> <SNIP>
>>>>> 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).
>>>>>
>>>>
>>>> Agreed.  Many quantum computers are machines that might produce the
>>>> right answer, and might produce a wrong answer.  The idea is that if
>>>> they give an answer fast enough, and you can check the answer reliably
>>>> and efficiently, then you can always run it again if it has got things
>>>> wrong.
>>>
>>> Why do you believe that quantum computers have any more theoretical
>>> computational capabilities than a water computer (built with tubes,
>>> water pressure source, and surface tension)?
>>
>> I don't believe that.  Why do you think I did?
> 
> Fair question. Since quantum computers (other than normal restrictions
> that arise from being finite) don't bring any new class of languages or
> capabilities to the table: So why mention them? My conjecture was that
> you must believe differently and I wanted to know why.

Certainly a lot of people do seem to believe that quantum computers can
solve problems that other computers cannot, or that they magically turn
NP problems into P problems.  (They don't, as long as you remember to
take scaling of machine size into account as well as time.  Shor's
algorithm, for example, is only polynomial time if you have an unlimited
size of quantum computer.  And if you are going to drop size
restrictions, then integer factorisation is O(1) on conventional
computers - you just need a /lot/ of dividers running in parallel.)


The one thing quantum computers do is bring a level of uncertainty and
non-determinism to the table.  For many of their setups and algorithms
(and this includes D-Wave's adiabatic quantum computers as well as
"true" quantum computers), a run of the system can stop and give an
output that is not actually the right answer.  (For adiabatic computers
running optimisation problems, it is unlikely ever to give the "right"
answer, i.e., the optimal solution.  But it can give better or worse
answers.)

So if you run your quantum computer on a particular problem and it gives
out the answer X, it might be correct or it might not be.  You have to
check it.  As long as the time to run the machine and check the answer,
scaled according to the probability of it giving the right answer, is
faster than the time taken for a conventional computer - then using the
unreliable quantum machine pays off.

There are other unreliable computation models that can be used.  You can
solve some optimisation problems by making a wire frame and dipping it
in a soap solution then examining the soap films produced.  Each run
will be very fast, but you might not get the right answer and have to
try again.

The thread branch here had been about functions whose output is not
reliable, but which might not be as useless as they first appear.
(Olcott and Flibble's partial halt deciders, however, /are/ useless.)


> 
>> But there are some types of problems which quantum computers could - in
>> theory - solve significantly faster than "conventional" computers.
>> Often, however, they only give something that /might/ be the answer you
>> want and so you have to check it.  If you are lucky, you've got the
>> answer - if not, you try again.
> 
> I think that quantum technology is/will be quite a bit more reliable
> than the stuff we are using now. To test this we would need to compare
> the probability of a Q finishing in the wrong state and compare that,
> using mean time to failure statistics and length of computation, to get
> failure probability for a standard computation. I'm betting on Q being
> more reliable while at the same time admitting that I'm decades past the
> point where I could try to do the arithmetic.
> 
> If my belief is correct, one should start doing verification of all
> important computational results and that, perhaps, isn't so bad an idea.
> After all, many critical computer systems do redundant calculations,
> voting results, and some even use alternative calculations to do
> checking. Some example domains are avionics and nuclear plant control.

I work with embedded software in control applications.  I don't often
have to deal with safety systems, but I do so occasionally - yes,
redundancy and checking is vital (as is finding a way to make sure your
discrepancy resolution systems are reliable...).  And anyone who has
lost data to a hard disk failure knows you need backups of your backups!

> There are many others. Once again, I don't think that quantum changes
> much besides what we can do with serious speed increase.
> 

I don't think quantum computers will actually be useful for anything,
unless you call "persuading governments and large companies to give you
lots of money" useful.  Playing with them has lead to a lot of
interesting physics, engineering and mathematics, but I don't foresee
them reaching a point where it is faster and cheaper to use a quantum
computer to solve a given problem than using conventional computers.

There are plenty of people telling us how wonderful quantum computers
are going to be - alternatively, how terrible they will be because they
will break the encryption of the internet.  They will then offer to sell
you a 5,000,000 dollar device that can sometimes solve a few problems
faster than a 500 dollar PC - or their new "post quantum" encryption
algorithm that has not been tested in the wild.

In reality, Shor's algorithm has been used in practice on quantum
computers to factor 21.  Not 21 digit numbers - the number 21.  IBM
tried to factor 35, but it was too difficult and the errors accumulated
too quickly.

My prediction is that fission generators will be common-place before
useful quantum computers.


>>> If you check the answer reliably -- possibilities = yes and no -- then
>>> you are done and need nothing else. Correct?-- 
> Jeff Barnett
>

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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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