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computers / comp.ai.philosophy / Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)

SubjectAuthor
* Happy Thanksgiving to allolcott
`* Re: Happy Thanksgiving to allolcott
 +* Re: Happy Thanksgiving to allolcott
 |+- Re: Happy Thanksgiving to allolcott
 |`* Re: Happy Thanksgiving to allolcott
 | `* Re: Happy Thanksgiving to allolcott
 |  +- Re: Happy Thanksgiving to all (over your head)olcott
 |  `* Re: Happy Thanksgiving to all (Over your head)olcott
 |   +* Re: Happy Thanksgiving to all (Over your head)olcott
 |   |`* Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | +* Re: Happy Thanksgiving to all (logical necessity)Mr Flibble
 |   | |`- Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | +* Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | |+* Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | ||`- Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | |`- Re: Happy Thanksgiving to all (logical necessity)olcott
 |   | `- Re: Happy Thanksgiving to all (logical necessity)olcott
 |   `* Re: Happy Thanksgiving to all (Over your head)Jeff Barnett
 |    `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |     `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      +* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |`* Re: Happy Thanksgiving to all (logical necessity)Jeff Barnett
 |      | `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |  `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |   +- Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |   `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |    `* Re: Happy Thanksgiving to all (logical necessity)olcott
 |      |     +* Re: Happy Thanksgiving to all (logical necessity)(asleep at the switch)olcott
 |      |     |+* Re: Happy Thanksgiving to all (logical necessity)(asleep at theolcott
 |      |     ||`* Re: Happy Thanksgiving to all (logical necessity)(asleep at theChris M. Thomasson
 |      |     || `* Re: Happy Thanksgiving to all (logical necessity)(asleep at theJeff Barnett
 |      |     ||  `* Re: Happy Thanksgiving to all (logical necessity)(asleep at theChris M. Thomasson
 |      |     ||   `- Re: Happy Thanksgiving to all (logical necessity)(asleep at theJeff Barnett
 |      |     |+* Re: Happy Thanksgiving to all (logical necessity)(asleep at the switch)olcott
 |      |     ||`* Re: Happy Thanksgiving to all (logical necessity)(asleep at theKaz Kylheku
 |      |     || `* Re: Happy Thanksgiving to all (logical necessity)(asleep at theolcott
 |      |     ||  `* Re: Happy Thanksgiving to all (logical necessity)(asleep at theKaz Kylheku
 |      |     ||   +* Re: Happy Thanksgiving to all (logical necessity)(asleep at theolcott
 |      |     ||   |`- Re: Happy Thanksgiving to all (logical necessity)(asleep at the switch)olcott
 |      |     ||   `- Re: Happy Thanksgiving to all (logical necessity)(asleep at theolcott
 |      |     |`* Re: Happy Thanksgiving to all (logical necessity)(Numbskull?)olcott
 |      |     | +* Re: Happy Thanksgiving to all (logical necessity)[ Ben is a Numbskull !!! olcott
 |      |     | |`* Re: Happy Thanksgiving to all (logical necessity)[ Ben is a Numbskullolcott
 |      |     | | `- Re: Happy Thanksgiving to all (logical necessity)[ Ben is a Numbskullolcott
 |      |     | +* Re: Happy Thanksgiving to all (logical necessity)(Numbskull?)olcott
 |      |     | |`* Re: Refuting the Peter Linz HP proofolcott
 |      |     | | `* Re: Refuting the Peter Linz HP proofolcott
 |      |     | |  `* Re: Refuting the Peter Linz HP proofolcott
 |      |     | |   `- Re: Refuting the Peter Linz HP proofolcott
 |      |     | +* Re: Happy Thanksgiving to all (logical necessity)[ Effectiveolcott
 |      |     | |+- Re: Local halt decider enabled[ Effective Presentation ]olcott
 |      |     | |`* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | | `* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  +- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  +* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  |+- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  |+* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||`* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  || +* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  || |`- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  || `* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||  `* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||   `* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||    `* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||     +- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||     +- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||     +* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||     |`* Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  ||     | `* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  +* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]Mr Flibble
 |      |     | |  ||     |  |`* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  | `- Re: Refutation of Peter Linz HP proof [ Logical Necessity ]Jeff Barnett
 |      |     | |  ||     |  +* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  |+* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  ||`* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]Kaz Kylheku
 |      |     | |  ||     |  || `* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  ||  `* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]Kaz Kylheku
 |      |     | |  ||     |  ||   `* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  ||    `* Re: Refutation of Peter Linz HP proof [ Logical Necessity ]Kaz Kylheku
 |      |     | |  ||     |  ||     `* Re: Refutation of Peter Linz HP proof [ divide by zero error returnsolcott
 |      |     | |  ||     |  ||      `* Re: Refutation of Peter Linz HP proof [ divide by zero errorKaz Kylheku
 |      |     | |  ||     |  ||       `- Re: Refutation of Peter Linz HP proof [ divide by zero error returnsolcott
 |      |     | |  ||     |  |+- Re: Refutation of Peter Linz HP proof [ Logical Necessity ]olcott
 |      |     | |  ||     |  |`* Re: Refutation of Peter Linz HP proof [ Recursion with TMs ]olcott
 |      |     | |  ||     |  | `* Re: Refutation of Peter Linz HP proof [ Recursion with TMs ]olcott
 |      |     | |  ||     |  |  `* Re: Refutation of Peter Linz HP proof [ Recursion with TMs ]olcott
 |      |     | |  ||     |  |   `- Re: Refutation of Peter Linz HP proof [ Recursion with TMs ]Mr Flibble
 |      |     | |  ||     |  `* Re: Refutation of Peter Linz HP proof [ Dishonest dodges ]olcott
 |      |     | |  ||     |   `- Re: Refutation of Peter Linz HP proof [ Dishonest dodges ]olcott
 |      |     | |  ||     `* Re: Renaming DebugTrace() to H or Halts[ Halts == Simulate ]olcott
 |      |     | |  ||      `* Re: Renaming DebugTrace() to H or Halts[ Halts == Simulate ]olcott
 |      |     | |  ||       `- Re: Renaming DebugTrace() to H or Halts[ Halts == Simulate ]olcott
 |      |     | |  |`- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  +- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | |  `- Re: Renaming DebugTrace() to H or Halts[ Effective Presentation ]olcott
 |      |     | `* Re: Happy Thanksgiving to all (logical necessity)(Numbskull?)olcott
 |      |     |  `* Re: Happy Thanksgiving to all (logical necessity)(Numbskull?)olcott
 |      |     |   +* Re: Both invocations of Confound_Halts() are decided consistentlyolcott
 |      |     |   |`- Re: Both invocations of Confound_Halts() are decided consistentlyolcott
 |      |     |   `- Re: Happy Thanksgiving to all (logical necessity)(Over Ben's head)olcott
 |      |     +* Re: Happy Thanksgiving to all (Ben is proven wrong by the actual facts)olcott
 |      |     +- Re: Happy Thanksgiving to all (Ben is proven wrong by the actualolcott
 |      |     `* Re: Happy Thanksgiving to all (Ben is proven wrong by the actual facts)olcott
 |      `* Re: Happy Thanksgiving to all (logical necessity)Jeff Barnett
 `* Re: Happy Thanksgiving to allKaz Kylheku

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Subject: Re: Refuting the Peter Linz HP Proof
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 01:08 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!news.uzoreto.com!tr3.eu1.usenetexpress.com!feeder.usenetexpress.com!tr3.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Fri, 11 Dec 2020 19:08:01 -0600
Subject: Re: Refuting the Peter Linz HP Proof
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <dcedna86RIORjUzCnZ2dnUU7-LWdnZ2d@giganews.com> <PHkAH.100296$ca39.31999@fx28.ams4> <SY6dnSQQp94TsE_CnZ2dnUU7-cHNnZ2d@giganews.com> <20201210104728.683@kylheku.com> <1cSdnVqvb_qhG0_CnZ2dnUU7-f3NnZ2d@giganews.com> <20201210141118.816@kylheku.com> <Rv2dnRr_Nd_7N0_CnZ2dnUU7-IfNnZ2d@giganews.com> <20201210151144.701@kylheku.com> <WYKdnfylBcYSMk_CnZ2dnUU7-a3NnZ2d@giganews.com> <20201210165018.816@kylheku.com> <-7WdnWdBCsMRWk_CnZ2dnUU7-b3NnZ2d@giganews.com> <rqvl9a$18v0$1@gioia.aioe.org> <sdednfBvJo5k407CnZ2dnUU7-SvNnZ2d@giganews.com> <xrLAH.74230$oqF7.23434@fx32.ams4> <J5KdnZGIktsAGU7CnZ2dnUU7-ffNnZ2d@giganews.com> <AILAH.352084$IbZ9.178036@fx10.ams4> <yPadnXJ3aL-nFk7CnZ2dnUU7-a3NnZ2d@giganews.com> <LZLAH.292683$kpV8.165984@fx36.ams4> <T6idnQl92u7vDU7CnZ2dnUU7-IXNnZ2d@giganews.com> <cc413e3a-fe7f-49a8-a7f7-afbceb7bae6bn@googlegroups.com> <ko-dnT5xm7mGAE7CnZ2dnUU7-VWdnZ2d@giganews.com> <rr14lv$1gpk$1@gioia.aioe.org>
From: NoO...@NoWhere.com (olcott)
Date: Fri, 11 Dec 2020 19:08:00 -0600
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.5.1
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On 12/11/2020 6:59 PM, Chris M. Thomasson wrote:
On 12/11/2020 8:23 AM, olcott wrote:
On 12/11/2020 10:04 AM, Malcolm McLean wrote:
On Friday, 11 December 2020 at 15:30:02 UTC, olcott wrote:
On 12/11/2020 9:10 AM, Mr Flibble wrote:
On 11/12/2020 15:07, olcott wrote:
On 12/11/2020 8:52 AM, Mr Flibble wrote:

The difference between refuting a proof by showing how its
counter-example basis of undecidability can be decided is not the same
thing as solving the halting problem.

Your argument is specious. Refuting Turing's proof is EQUIVALENT to
solving the HP. The HP cannot be solved.

This is factually false.
Refuting the proof requires proving that the one counter-example of
undecidability used in the proof is decidable.

Solving the halting problem requires proving that every counter-example
that can possibly exist is decidable.

You're right here.
But you've flip-flopped on whether you have an H / H_Hat pair, or a full
halt decider.


Since I am not all knowing I have always only had a partial decider.


I have a partial decider. You will give up in less than two months... Halt. Am I right? Passing on to your decider... ;^)

12,000 messages from me in the comp.theory forum since 2004 say otherwise.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 01:10 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Fri, 11 Dec 2020 19:10:52 -0600
Subject: Re: Refuting the Peter Linz HP Proof
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<PHkAH.100296$ca39.31999@fx28.ams4>
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<WYKdnfylBcYSMk_CnZ2dnUU7-a3NnZ2d@giganews.com>
<20201210165018.816@kylheku.com>
<-7WdnWdBCsMRWk_CnZ2dnUU7-b3NnZ2d@giganews.com>
<rqvl9a$18v0$1@gioia.aioe.org>
<sdednfBvJo5k407CnZ2dnUU7-SvNnZ2d@giganews.com>
<xrLAH.74230$oqF7.23434@fx32.ams4>
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<LZLAH.292683$kpV8.165984@fx36.ams4>
<T6idnQl92u7vDU7CnZ2dnUU7-IXNnZ2d@giganews.com>
<cc413e3a-fe7f-49a8-a7f7-afbceb7bae6bn@googlegroups.com>
<ko-dnT5xm7mGAE7CnZ2dnUU7-VWdnZ2d@giganews.com>
<rr14lv$1gpk$1@gioia.aioe.org>
<q7OdnSAe2fpviknCnZ2dnUU7-LmdnZ2d@giganews.com>
From: NoO...@NoWhere.com (olcott)
Date: Fri, 11 Dec 2020 19:10:51 -0600
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On 12/11/2020 7:08 PM, olcott wrote:
On 12/11/2020 6:59 PM, Chris M. Thomasson wrote:
On 12/11/2020 8:23 AM, olcott wrote:
On 12/11/2020 10:04 AM, Malcolm McLean wrote:
On Friday, 11 December 2020 at 15:30:02 UTC, olcott wrote:
On 12/11/2020 9:10 AM, Mr Flibble wrote:
On 11/12/2020 15:07, olcott wrote:
On 12/11/2020 8:52 AM, Mr Flibble wrote:

The difference between refuting a proof by showing how its
counter-example basis of undecidability can be decided is not the same
thing as solving the halting problem.

Your argument is specious. Refuting Turing's proof is EQUIVALENT to
solving the HP. The HP cannot be solved.

This is factually false.
Refuting the proof requires proving that the one counter-example of
undecidability used in the proof is decidable.

Solving the halting problem requires proving that every counter-example
that can possibly exist is decidable.

You're right here.
But you've flip-flopped on whether you have an H / H_Hat pair, or a full
halt decider.


Since I am not all knowing I have always only had a partial decider.


I have a partial decider. You will give up in less than two months... Halt. Am I right? Passing on to your decider... ;^)

12,000 messages from me in the comp.theory forum since 2004 say otherwise.


12,743 messages from me in the comp.theory forum since 2004 say otherwise.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 01:16 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Fri, 11 Dec 2020 19:16:24 -0600
Subject: Re: Refuting the Peter Linz HP Proof
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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<20201210151144.701@kylheku.com>
<WYKdnfylBcYSMk_CnZ2dnUU7-a3NnZ2d@giganews.com>
<20201210165018.816@kylheku.com>
<-7WdnWdBCsMRWk_CnZ2dnUU7-b3NnZ2d@giganews.com>
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<20201211105615.439@kylheku.com>
<rf6dnQqaD69bWE7CnZ2dnUU7-fvNnZ2d@giganews.com>
<20201211114017.28@kylheku.com>
<DK2dndUXY-r_Uk7CnZ2dnUU7-V_NnZ2d@giganews.com>
<20201211120229.239@kylheku.com>
<zKWdneCFKdINSU7CnZ2dnUU7-YnNnZ2d@giganews.com>
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From: NoO...@NoWhere.com (olcott)
Date: Fri, 11 Dec 2020 19:16:23 -0600
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On 12/11/2020 7:00 PM, Kaz Kylheku wrote:
["Followup-To:" header set to comp.theory.]
On 2020-12-12, olcott <NoOne@NoWhere.com> wrote:
On 12/11/2020 6:19 PM, Kaz Kylheku wrote:
On 2020-12-11, olcott <NoOne@NoWhere.com> wrote:
Halts() returns to main().

Halts(P, P) terminates, yay!

No function ever returns any value to its infinite invocation thus
Halts() never returns any value to H_Hat().

Wait, Halts(P, P) does not terminate.


The Halts() called by main() terminates returning its result to main()
after aborting the infinitely recursive invocation of Halts by H_Hat().

The Halts which is called by H_Hat also perpetrates an infinite
recursive invocation of Halst by H_Hat.  Yet *that* Halts doesn't
abort anything and is not able to return.

So, the two (Halts called from main, and Halts called from H_Hat)
are not the same function. One aborts an infinitely recursive
invocation, whereas the other does not.


There is only one Halts() function at a single machine address.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof
From: Kaz Kylheku
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Followup: comp.theory
Organization: Aioe.org NNTP Server
Date: Sat, 12 Dec 2020 02:13 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Path: i2pn2.org!i2pn.org!aioe.org!opIzC+UpU1FF0qsNaB+JHA.user.gioia.aioe.org.POSTED!not-for-mail
From: 563-365-...@kylheku.com (Kaz Kylheku)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
Subject: Re: Refuting the Peter Linz HP Proof
Followup-To: comp.theory
Date: Sat, 12 Dec 2020 02:13:39 +0000 (UTC)
Organization: Aioe.org NNTP Server
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["Followup-To:" header set to comp.theory.]
On 2020-12-12, olcott <NoOne@NoWhere.com> wrote:
On 12/11/2020 7:00 PM, Kaz Kylheku wrote:
["Followup-To:" header set to comp.theory.]
On 2020-12-12, olcott <NoOne@NoWhere.com> wrote:
On 12/11/2020 6:19 PM, Kaz Kylheku wrote:
On 2020-12-11, olcott <NoOne@NoWhere.com> wrote:
Halts() returns to main().

Halts(P, P) terminates, yay!

No function ever returns any value to its infinite invocation thus
Halts() never returns any value to H_Hat().

Wait, Halts(P, P) does not terminate.


The Halts() called by main() terminates returning its result to main()
after aborting the infinitely recursive invocation of Halts by H_Hat().

The Halts which is called by H_Hat also perpetrates an infinite
recursive invocation of Halst by H_Hat.  Yet *that* Halts doesn't
abort anything and is not able to return.

So, the two (Halts called from main, and Halts called from H_Hat)
are not the same function. One aborts an infinitely recursive
invocation, whereas the other does not.


There is only one Halts() function at a single machine address.

If the code at that address changes its behavior based on any
context information that is not carried in its aguments, it is not
a function. Or, it is not a function *of those arguments*, anyway.

If such a thing is going on, we have to examine it more closely,
to determine whether we can still regard it as a function.

Every function has an implicit parameter, which is is its dynamic
environment. Roughly speaking, it consists of everyhing which is
in the activation chain produced by the callers of that function.

A function call like F(X) could change its behavior based on that
environment.

In that case, we can no longer think of it as a one-argument function.

But what we can do is make explicit the environment argument, and
regard the function call as being:

  F(E, X).

E carries the information which allows F to return to the correct caller
and such (the "continuation"). Thus, but inspecting the environment E, F
can behave differently based on the identity of its caller (e.g. main or
H_Hat).

Thus if F(X) is called from two different places, then one of those
calls is actually F(E1, X), and the other is F(E2, X) when we reveal the
hidden environment parameter. Then we see they are not the same
function.

Normally, the functions in the programming language are "well-behaved"
and don't do such a thing; their behavior is independent of E, and so
the language can treat it as a hidden argument. The code generation
mainains a "stack pointer", for instance, which is a de facto
argument being passed down, but it's not visible in in the higher
level language.

--
TXR Programming Language: http://nongnu.org/txr


Subject: Re: Refuting the Peter Linz HP Proof
From: Kaz Kylheku
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Followup: comp.theory
Organization: Aioe.org NNTP Server
Date: Sat, 12 Dec 2020 02:18 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Path: i2pn2.org!i2pn.org!aioe.org!opIzC+UpU1FF0qsNaB+JHA.user.gioia.aioe.org.POSTED!not-for-mail
From: 563-365-...@kylheku.com (Kaz Kylheku)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
Subject: Re: Refuting the Peter Linz HP Proof
Followup-To: comp.theory
Date: Sat, 12 Dec 2020 02:18:24 +0000 (UTC)
Organization: Aioe.org NNTP Server
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On 2020-12-12, olcott <NoOne@NoWhere.com> wrote:
On 12/11/2020 7:00 PM, Kaz Kylheku wrote:
["Followup-To:" header set to comp.theory.]
On 2020-12-12, olcott <NoOne@NoWhere.com> wrote:
On 12/11/2020 6:19 PM, Kaz Kylheku wrote:
On 2020-12-11, olcott <NoOne@NoWhere.com> wrote:
Halts() returns to main().

Halts(P, P) terminates, yay!

No function ever returns any value to its infinite invocation thus
Halts() never returns any value to H_Hat().

Wait, Halts(P, P) does not terminate.


The Halts() called by main() terminates returning its result to main()
after aborting the infinitely recursive invocation of Halts by H_Hat().

The Halts which is called by H_Hat also perpetrates an infinite
recursive invocation of Halst by H_Hat.  Yet *that* Halts doesn't
abort anything and is not able to return.

So, the two (Halts called from main, and Halts called from H_Hat)
are not the same function. One aborts an infinitely recursive
invocation, whereas the other does not.


There is only one Halts() function at a single machine address.

By he way, did you see my program? It also has a single Halts
function.

It shows that H_Hat(H_Hat) halts, and that Halts(H_Hat, H_Hat)
decides that.

How does it do so? Environment inspection.

Just like your solution with its DebugTrace call, mine uses a debug
tracing facility: the calculation of a backtrace.

The backtrace function (available in the GNU C library in GNU/Linux
systems) has access to the hidden dynamic environment parameter which
can distinguish how a function is called, such as what are its callers.

The new program you allegedly have is pulling the same sort of
shennanigan.

#include <stdio.h>
#include <execinfo.h>

typedef void (*fun_t)(void *data);
typedef int (*decider_t)(fun_t, void *data);

int Halts(fun_t, void *);

void H_Hat(void *data)
{
  if (Halts((fun_t) data, data)) {
    for (;;)
      fflush(stdout);
  } else {
    return;
  }
}

int Halts(fun_t fun, void *data)
{
  void *buffer[10];
  int i, ncallers = backtrace(buffer, 10);

  (void) fun;
  (void) data;

  for (i = 0; i < ncallers; i++)
    if (buffer[i] >= (void *) H_Hat && buffer[i] < (void *) Halts)
      return 0;

  return 1;
}

int main(void)
{
  H_Hat((void *) H_Hat);

  puts("Got here so H_Hat(H_Hat) halted!");

  if (Halts(H_Hat, (void *) H_Hat))
    puts("H_Hat(H_Hat) halts!");
  else
    puts("H_Hat(H_Hat) doesn't halt!");

  return 0;
}

--
TXR Programming Language: http://nongnu.org/txr


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 15:31 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 09:31:51 -0600
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
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From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 09:31:50 -0600
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On 12/12/2020 8:10 AM, André G. Isaak wrote:
On 2020-12-12 07:02, olcott wrote:
On 12/12/2020 7:57 AM, André G. Isaak wrote:
On 2020-12-12 06:51, olcott wrote:
On 12/11/2020 11:47 PM, André G. Isaak wrote:
On 2020-12-11 22:33, olcott wrote:

<snippage>

int Add(int X, int Y)
{
   return Add(X, Y);
}

int main()
{
    while(1)
      int Z = Add(5,3);
}

The first machine always halts until another machine loops it.


As far as I can tell, the first machine never halts. And I have no idea what point you are trying to make or how it relates to the definition of 'decider'.

André

If a decider is contained within an infinite loop then the decider never halts.


Let's assume your first machine was intended to be the following rather than the infinitely recursive routine you give above.

int Add(int x, int y) {
     return(x + y);
}

Putting this in a loop as above means that *main* doesn't halt. Add() returns a value every time it is called; ergo it halts.

André


When main() puts the decider Add() in an infinite loop Add() is still a decider. When H_Hat() puts Halts() in infinite recursion Halts() is still a decider.

A decider, *by definition*, must complete its computation and return a value to its caller; Putting Add() in an infinite loop doesn't prevent it from doing this. Infinite recursion does. If your Halts() gets stuck in infinite recursion such that it doesn't return a value to its caller, then it is *not* a decider.

You really ought to learn basic definitions before you set out to refute well-established theorems. If you don't even understand what a decider is, how do you plan on constructing one?

André


When a decider does not return a value to its caller only because its caller invoked this decider in infinite recursion this decider is still a decider even though it does not return any value to its caller.



--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing machines ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 16:13 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 10:13:36 -0600
Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing
machines ]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<20201209083459.847@kylheku.com>
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From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 10:13:35 -0600
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On 12/12/2020 9:43 AM, Malcolm McLean wrote:
On Saturday, 12 December 2020 at 15:08:56 UTC, André G. Isaak wrote:
On 2020-12-12 07:38, olcott wrote:

Because it does correctly decide halting it <is> a halting decider no
matter what conventional terminology says to the contrary.
Look, words actually *mean* things, and in technical fields they usually
mean very precise things. If your program is not guaranteed to return a
result to its caller, then it is not a decider, period.

It's a cheat. It's making a decision, but not returning it to caller.


If software engineering knows that infinite recursion never returns a result to its caller and computer science does not know this then this would be ignorance on the part of computer science.

It may be the case that no one ever got around to analyzing the case of infinitely recursive Turing machines where UTM X simulates UTM Y that simulates UTM X.

But no-one with any sense, when offered a refutation of Turing's proof
that halting is decideable, would expect anything other than a cheat.

You have to cut PO a bit of slack.



--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 16:24 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 10:24:39 -0600
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<XPadnSPi4dGOeU3CnZ2dnUU7-VXNnZ2d@giganews.com>
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From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 10:24:38 -0600
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On 12/12/2020 9:49 AM, André G. Isaak wrote:
On 2020-12-12 08:31, olcott wrote:
On 12/12/2020 8:10 AM, André G. Isaak wrote:
On 2020-12-12 07:02, olcott wrote:
On 12/12/2020 7:57 AM, André G. Isaak wrote:
On 2020-12-12 06:51, olcott wrote:
On 12/11/2020 11:47 PM, André G. Isaak wrote:
On 2020-12-11 22:33, olcott wrote:

<snippage>

int Add(int X, int Y)
{
   return Add(X, Y);
}

int main()
{
    while(1)
      int Z = Add(5,3);
}

The first machine always halts until another machine loops it.


As far as I can tell, the first machine never halts. And I have no idea what point you are trying to make or how it relates to the definition of 'decider'.

André

If a decider is contained within an infinite loop then the decider never halts.


Let's assume your first machine was intended to be the following rather than the infinitely recursive routine you give above.

int Add(int x, int y) {
     return(x + y);
}

Putting this in a loop as above means that *main* doesn't halt. Add() returns a value every time it is called; ergo it halts.

André


When main() puts the decider Add() in an infinite loop Add() is still a decider. When H_Hat() puts Halts() in infinite recursion Halts() is still a decider.

A decider, *by definition*, must complete its computation and return a value to its caller; Putting Add() in an infinite loop doesn't prevent it from doing this. Infinite recursion does. If your Halts() gets stuck in infinite recursion such that it doesn't return a value to its caller, then it is *not* a decider.

You really ought to learn basic definitions before you set out to refute well-established theorems. If you don't even understand what a decider is, how do you plan on constructing one?

André


When a decider does not return a value to its caller only because its caller invoked this decider in infinite recursion this decider is still a decider even though it does not return any value to its caller.

A decider must return a yes or no value for *every possible* input. If there are inputs which can lead to infinite recursion then it does not return a value for every possible input. The fact that there are inputs that can lead to infinite recursion means your "decider" is broken (i.e. is not a decider).


The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

If software engineering knows that infinite recursion never returns a result to its caller and computer science does not know this then this would be ignorance on the part of computer science.

It may be the case that no one ever got around to analyzing the case of infinitely recursive Turing machines where UTM X simulates UTM Y that simulates UTM X.

You can't simply redefine what a decider is by declaring that certain instances of not returning a value "don't count" and still claim your results to have any relevance to proofs about actual deciders.

André


If it decides (halts and returns Boolean) some inputs then it <is> a (conventional) decider for these inputs.

If it decides (halts and returns Boolean) for some invocations on some inputs then it <is> a (conventional) decider for these invocations on these inputs.

The outermost invocation of Halts always returns Boolean to its caller thus proving that this invocation of Halts() <is> a decider even if it must abort the simulations of infinitely recursive inner invocations of itself.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing machines ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 16:29 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 10:29:05 -0600
Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing
machines ]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<BuCdnWJkOZM4NUzCnZ2dnUU7-UPNnZ2d@giganews.com> <rqsgm9$1c0$1@dont-email.me>
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<473419c4-3ee0-4140-b070-0fde79bc039dn@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 10:29:04 -0600
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On 12/12/2020 10:20 AM, Malcolm McLean wrote:
On Saturday, 12 December 2020 at 16:13:43 UTC, olcott wrote:
On 12/12/2020 9:43 AM, Malcolm McLean wrote:
On Saturday, 12 December 2020 at 15:08:56 UTC, André G. Isaak wrote:
On 2020-12-12 07:38, olcott wrote:

Because it does correctly decide halting it <is> a halting decider no
matter what conventional terminology says to the contrary.
Look, words actually *mean* things, and in technical fields they usually
mean very precise things. If your program is not guaranteed to return a
result to its caller, then it is not a decider, period.

It's a cheat. It's making a decision, but not returning it to caller.

If software engineering knows that infinite recursion never returns a
result to its caller and computer science does not know this then this
would be ignorance on the part of computer science.

It may be the case that no one ever got around to analyzing the case of
infinitely recursive Turing machines where UTM X simulates UTM Y that
simulates UTM X.
But no-one with any sense, when offered a refutation of Turing's proof
that halting is decideable, would expect anything other than a cheat.

You have to cut PO a bit of slack.


You provided H. So if H goes off into infinite recursion when passed some
parameters, that's because you wrote H in that way. Having said that,
it's hardly surprising if H goes into infinite recursion if fed an input
containing H itself.

So you get an external supervisor, which is the same source as H, to terminate
the recursion. But you now don't have the set-up demanded by Linz.


That does not matter as long as this global halt decider has no inputs that can be shown to be undecidable {Linz, Sipser and Kozen} are refuted indirectly in that they claim undecidable inputs exist.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing machines ]
From: Mr Flibble
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Organization: Jupiter Mining Corporation
Date: Sat, 12 Dec 2020 16:41 UTC
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Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing
machines ]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
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From: flib...@i42.REMOVETHISBIT.co.uk (Mr Flibble)
Organization: Jupiter Mining Corporation
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On 12/12/2020 16:13, olcott wrote:
On 12/12/2020 9:43 AM, Malcolm McLean wrote:
On Saturday, 12 December 2020 at 15:08:56 UTC, André G. Isaak wrote:
On 2020-12-12 07:38, olcott wrote:

Because it does correctly decide halting it <is> a halting decider no
matter what conventional terminology says to the contrary.
Look, words actually *mean* things, and in technical fields they usually
mean very precise things. If your program is not guaranteed to return a
result to its caller, then it is not a decider, period.

It's a cheat. It's making a decision, but not returning it to caller.


If software engineering knows that infinite recursion never returns a result to its caller and computer science does not know this then this would be ignorance on the part of computer science.

To refute Turing's proof and solve the halting problem you have to be able to detect infinite recursion which INCLUDES CONDITIONALS which you are not doing; what you are doing has no interest to computer science practitioners as you are not adding anything new of value.

/Flibble

--
😎


Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing machines ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 16:44 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 10:44:03 -0600
Subject: Re: Refuting the Peter Linz HP Proof [ infinitely recursive Turing machines ]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
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From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 10:44:03 -0600
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On 12/12/2020 10:41 AM, Mr Flibble wrote:
On 12/12/2020 16:13, olcott wrote:
On 12/12/2020 9:43 AM, Malcolm McLean wrote:
On Saturday, 12 December 2020 at 15:08:56 UTC, André G. Isaak wrote:
On 2020-12-12 07:38, olcott wrote:

Because it does correctly decide halting it <is> a halting decider no
matter what conventional terminology says to the contrary.
Look, words actually *mean* things, and in technical fields they usually
mean very precise things. If your program is not guaranteed to return a
result to its caller, then it is not a decider, period.

It's a cheat. It's making a decision, but not returning it to caller.


If software engineering knows that infinite recursion never returns a result to its caller and computer science does not know this then this would be ignorance on the part of computer science.

To refute Turing's proof and solve the halting problem you have to be able to detect infinite recursion which INCLUDES CONDITIONALS which you are not doing;

Right. To refute Turing's proof and bake a cake does not require examining conditionals, it does require baking a cake.

what you are doing has no interest to computer science practitioners as you are not adding anything new of value.

/Flibble



--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng, comp.software-eng
Date: Sat, 12 Dec 2020 17:38 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 11:38:33 -0600
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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<y-mdnYZJTZe2X0_CnZ2dnUU78XHNnZ2d@brightview.co.uk>
<20201211160902.199@kylheku.com>
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From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 11:38:32 -0600
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On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:
On 12/12/2020 9:49 AM, André G. Isaak wrote:
On 2020-12-12 08:31, olcott wrote:
On 12/12/2020 8:10 AM, André G. Isaak wrote:
On 2020-12-12 07:02, olcott wrote:
On 12/12/2020 7:57 AM, André G. Isaak wrote:
On 2020-12-12 06:51, olcott wrote:
On 12/11/2020 11:47 PM, André G. Isaak wrote:
On 2020-12-11 22:33, olcott wrote:

<snippage>

int Add(int X, int Y)
{
   return Add(X, Y);
}

int main()
{
    while(1)
      int Z = Add(5,3);
}

The first machine always halts until another machine loops it.


As far as I can tell, the first machine never halts. And I have no idea what point you are trying to make or how it relates to the definition of 'decider'.

André

If a decider is contained within an infinite loop then the decider never halts.


Let's assume your first machine was intended to be the following rather than the infinitely recursive routine you give above.

int Add(int x, int y) {
     return(x + y);
}

Putting this in a loop as above means that *main* doesn't halt. Add() returns a value every time it is called; ergo it halts.

André


When main() puts the decider Add() in an infinite loop Add() is still a decider. When H_Hat() puts Halts() in infinite recursion Halts() is still a decider.

A decider, *by definition*, must complete its computation and return a value to its caller; Putting Add() in an infinite loop doesn't prevent it from doing this. Infinite recursion does. If your Halts() gets stuck in infinite recursion such that it doesn't return a value to its caller, then it is *not* a decider.

You really ought to learn basic definitions before you set out to refute well-established theorems. If you don't even understand what a decider is, how do you plan on constructing one?

André


When a decider does not return a value to its caller only because its caller invoked this decider in infinite recursion this decider is still a decider even though it does not return any value to its caller.

A decider must return a yes or no value for *every possible* input. If there are inputs which can lead to infinite recursion then it does not return a value for every possible input. The fact that there are inputs that can lead to infinite recursion means your "decider" is broken (i.e. is not a decider).


The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

....in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 17:45 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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NNTP-Posting-Date: Sat, 12 Dec 2020 11:45:26 -0600
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <BuCdnWJkOZM4NUzCnZ2dnUU7-UPNnZ2d@giganews.com> <rqsgm9$1c0$1@dont-email.me> <k-mdnbejZqXEqU_CnZ2dnUU7-enNnZ2d@giganews.com> <rqte7r$t6s$1@dont-email.me> <87pn3h9ywh.fsf@bsb.me.uk> <20201210142425.635@kylheku.com> <y-mdnYZJTZe2X0_CnZ2dnUU78XHNnZ2d@brightview.co.uk> <20201211160902.199@kylheku.com> <85WdnaiDyqRbkUnCnZ2dnUU7-IXNnZ2d@giganews.com> <rr1i1r$cvt$1@dont-email.me> <FYednaMDdu1C0knCnZ2dnUU7-fPNnZ2d@giganews.com> <rr1keo$3je$1@dont-email.me> <oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com> <rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com> <rr2vb1$mhs$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 11:45:25 -0600
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On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: Mr Flibble
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Organization: Jupiter Mining Corporation
Date: Sat, 12 Dec 2020 17:55 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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<20201210142425.635@kylheku.com>
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<oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me>
<YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me>
<EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me>
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From: flib...@i42.REMOVETHISBIT.co.uk (Mr Flibble)
Organization: Jupiter Mining Corporation
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On 12/12/2020 17:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

I can only detect bullshit from one source: you, and my bullshit detector is NOT a partial detector.

/Flibble

--
😎


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 18:26 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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NNTP-Posting-Date: Sat, 12 Dec 2020 12:26:33 -0600
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <k-mdnbejZqXEqU_CnZ2dnUU7-enNnZ2d@giganews.com> <rqte7r$t6s$1@dont-email.me> <87pn3h9ywh.fsf@bsb.me.uk> <20201210142425.635@kylheku.com> <y-mdnYZJTZe2X0_CnZ2dnUU78XHNnZ2d@brightview.co.uk> <20201211160902.199@kylheku.com> <85WdnaiDyqRbkUnCnZ2dnUU7-IXNnZ2d@giganews.com> <rr1i1r$cvt$1@dont-email.me> <FYednaMDdu1C0knCnZ2dnUU7-fPNnZ2d@giganews.com> <rr1keo$3je$1@dont-email.me> <oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com> <rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com> <rr2vb1$mhs$1@dont-email.me> <SrSdnbIYprUrnEjCnZ2dnUU7-U2dnZ2d@giganews.com> <rr30u4$2ba$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 12:26:32 -0600
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On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: Mr Flibble
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Organization: Jupiter Mining Corporation
Date: Sat, 12 Dec 2020 19:01 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Path: i2pn2.org!i2pn.org!aioe.org!peer03.ams4!peer.am4.highwinds-media.com!news.highwinds-media.com!fx40.ams4.POSTED!not-for-mail
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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<20201210142425.635@kylheku.com>
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<oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me>
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<0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me>
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<BcSdnZTygJfElkjCnZ2dnUU7-UednZ2d@giganews.com>
From: flib...@i42.REMOVETHISBIT.co.uk (Mr Flibble)
Organization: Jupiter Mining Corporation
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On 12/12/2020 18:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

To refute Turing's proof and solve the halting problem you have to be able to detect infinite recursion which INCLUDES CONDITIONALS which you are not doing.

This is yet another reason why you do not have a HP decider of any kind: you have to be able to decide on algorithms that include branching logic and anything else has no value whatsoever as far as the HP is concerned.

/Flibble

--
😎


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Sat, 12 Dec 2020 20:01 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <85WdnaiDyqRbkUnCnZ2dnUU7-IXNnZ2d@giganews.com> <rr1i1r$cvt$1@dont-email.me> <FYednaMDdu1C0knCnZ2dnUU7-fPNnZ2d@giganews.com> <rr1keo$3je$1@dont-email.me> <oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com> <rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com> <rr2vb1$mhs$1@dont-email.me> <SrSdnbIYprUrnEjCnZ2dnUU7-U2dnZ2d@giganews.com> <rr30u4$2ba$1@dont-email.me> <BcSdnZTygJfElkjCnZ2dnUU7-UednZ2d@giganews.com> <rr340r$l9i$1@dont-email.me> <bo2dnRdK_KDeiEjCnZ2dnUU7-UnNnZ2d@giganews.com> <rr34ok$rof$1@dont-email.me> <oaedncLQ-96MhEjCnZ2dnUU7-WnNnZ2d@giganews.com> <rr36c2$7dk$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 14:01:43 -0600
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On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly beyond me.

I am saying that anything which has the possibility of getting caught in infinite recursion cannot return a result and therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect infinite recursion on itself and return its decision to its caller does not count.

Basically you are saying that it is wrong all of the time even though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return a result for *all* inputs. That's the definition of 'decider'. Something that only returns results in some instances is not a decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly decide that it has been infinitely invoked that even though this decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for other inputs, then this same idea can be extended to some invocations and not all invocations, otherwise correctly deciding infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a dollar. A partial decider is something that correctly decides some cases, not something which is a decider in some cases. Things are either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen} counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a decider in those cases. You could call it a partial decider, but not a decider.

However, in the case of your program, you can't even call it that because it sometimes returns and other times does not return *on the same input*. A partial decider is something which decides some set of inputs and fails to decide another, *disjoint* set of inputs. Something which gets different results for the same input isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that it has been invoked in infinite recursion it must fix the bug in this infinitely recursive invocation so that it can report its infinitely recursive invocation to its infinitely recursive caller, that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>


--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: Mr Flibble
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Organization: Jupiter Mining Corporation
Date: Sat, 12 Dec 2020 20:04 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Path: i2pn2.org!i2pn.org!aioe.org!peer02.ams4!peer.am4.highwinds-media.com!news.highwinds-media.com!fx49.ams4.POSTED!not-for-mail
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<rr1i1r$cvt$1@dont-email.me> <FYednaMDdu1C0knCnZ2dnUU7-fPNnZ2d@giganews.com>
<rr1keo$3je$1@dont-email.me> <oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com>
<rr1lhm$8ul$1@dont-email.me> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com>
<rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com>
<rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com>
<rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com>
<rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com>
<rr2vb1$mhs$1@dont-email.me> <SrSdnbIYprUrnEjCnZ2dnUU7-U2dnZ2d@giganews.com>
<rr30u4$2ba$1@dont-email.me> <BcSdnZTygJfElkjCnZ2dnUU7-UednZ2d@giganews.com>
<rr340r$l9i$1@dont-email.me> <bo2dnRdK_KDeiEjCnZ2dnUU7-UnNnZ2d@giganews.com>
<rr34ok$rof$1@dont-email.me> <oaedncLQ-96MhEjCnZ2dnUU7-WnNnZ2d@giganews.com>
<rr36c2$7dk$1@dont-email.me> <-LCdnQjCJqk1vEjCnZ2dnUU7-eXNnZ2d@giganews.com>
From: flib...@i42.REMOVETHISBIT.co.uk (Mr Flibble)
Organization: Jupiter Mining Corporation
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On 12/12/2020 20:01, olcott wrote:
On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly beyond me.

I am saying that anything which has the possibility of getting caught in infinite recursion cannot return a result and therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect infinite recursion on itself and return its decision to its caller does not count.

Basically you are saying that it is wrong all of the time even though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return a result for *all* inputs. That's the definition of 'decider'. Something that only returns results in some instances is not a decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly decide that it has been infinitely invoked that even though this decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for other inputs, then this same idea can be extended to some invocations and not all invocations, otherwise correctly deciding infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a dollar. A partial decider is something that correctly decides some cases, not something which is a decider in some cases. Things are either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen} counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a decider in those cases. You could call it a partial decider, but not a decider.

However, in the case of your program, you can't even call it that because it sometimes returns and other times does not return *on the same input*. A partial decider is something which decides some set of inputs and fails to decide another, *disjoint* set of inputs. Something which gets different results for the same input isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that it has been invoked in infinite recursion it must fix the bug in this infinitely recursive invocation so that it can report its infinitely recursive invocation to its infinitely recursive caller, that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>
  You do not have a HP decider of any kind: you have to be able to decide on algorithms that include branching logic and anything else has no value whatsoever as far as the HP is concerned.

/Flibble

--
😎


Subject: Re: Refuting the {Linz, Sipser, Kozen} HP Proofs
From: olcott
Newsgroups: comp.theory, comp.lang.c, comp.lang.c++, comp.ai.philosophy
Date: Sun, 13 Dec 2020 04:50 UTC
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NNTP-Posting-Date: Sat, 12 Dec 2020 22:50:51 -0600
Subject: Re: Refuting the {Linz, Sipser, Kozen} HP Proofs
Newsgroups: comp.theory,comp.lang.c,comp.lang.c++,comp.ai.philosophy
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <AyQxH.181169$xe4.7725@fx41.iad> <ubmdnZBU3N5zSlrCnZ2dnUU7-KFQAAAA@giganews.com> <neRxH.214851$2j.16728@fx38.iad> <DZudnfRm5ZaoelrCnZ2dnUU7-W_NnZ2d@giganews.com> <HxSxH.34144$Oa.28187@fx16.iad> <ZMOdncRH0J-RZVrCnZ2dnUU7-TudnZ2d@giganews.com> <20201202130444.97@kylheku.com> <4ISdnZjauficjlXCnZ2dnUU7-X3NnZ2d@giganews.com> <20201202170501.883@kylheku.com> <rqbjrt$1s4o$1@gioia.aioe.org> <20201207211640.ab3cf977e95bac160b406d58@gmail.com> <87lfe9mat5.fsf@bsb.me.uk> <20201209144312.3fa9e12d9eb9f6e65a6bf909@gmail.com> <XPadnSPi4dGOeU3CnZ2dnUU7-VXNnZ2d@giganews.com> <20201209083459.847@kylheku.com> <bu6dnRRFqcQwjEzCnZ2dnUU7-UfNnZ2d@giganews.com> <rqs8jr$bq2$1@dont-email.me> <BuCdnWJkOZM4NUzCnZ2dnUU7-UPNnZ2d@giganews.com> <87im99c2hb.fsf@bsb.me.uk> <7u-dnZSkbvkIqE_CnZ2dnUU7-LHNnZ2d@giganews.com> <87v9d99zm2.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Sat, 12 Dec 2020 22:50:50 -0600
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On 12/10/2020 2:26 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

On 12/10/2020 5:41 AM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

Think of this is simpler terms:
I have an x86 emulator that aborts infinite loops and infinite
recursion.

A ridiculously trivial claim.  You really need to take care with your
language.


You are a master of deception of avoiding the point:

I am just pointing out you need to say what you mean.  Having an x86
emulator that aborts infinite loops and infinite recursion is trivial
and (I hope) not what you think you have.


Having an equivalent computation to the {Linz, Sipser} H correctly deciding the Linz Ĥ, the Sipser D and the Kozen N is what I have.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the {Linz, Sipser, Kozen} HP Proofs
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.lang.c, comp.lang.c++
Followup: comp.theory
Date: Mon, 14 Dec 2020 05:19 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
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NNTP-Posting-Date: Sun, 13 Dec 2020 23:20:00 -0600
Subject: Re: Refuting the {Linz, Sipser, Kozen} HP Proofs
Newsgroups: comp.theory,comp.ai.philosophy,comp.lang.c,comp.lang.c++
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
<neRxH.214851$2j.16728@fx38.iad>
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<HxSxH.34144$Oa.28187@fx16.iad>
<ZMOdncRH0J-RZVrCnZ2dnUU7-TudnZ2d@giganews.com>
<20201202130444.97@kylheku.com>
<4ISdnZjauficjlXCnZ2dnUU7-X3NnZ2d@giganews.com>
<20201202170501.883@kylheku.com> <rqbjrt$1s4o$1@gioia.aioe.org>
<20201207211640.ab3cf977e95bac160b406d58@gmail.com>
<87lfe9mat5.fsf@bsb.me.uk>
<20201209144312.3fa9e12d9eb9f6e65a6bf909@gmail.com>
<XPadnSPi4dGOeU3CnZ2dnUU7-VXNnZ2d@giganews.com>
<20201209083459.847@kylheku.com>
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Followup-To: comp.theory
From: NoO...@NoWhere.com (olcott)
Date: Sun, 13 Dec 2020 23:19:58 -0600
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On 12/13/2020 7:14 AM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

On 12/10/2020 2:26 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

On 12/10/2020 5:41 AM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

Think of this is simpler terms:
I have an x86 emulator that aborts infinite loops and infinite
recursion.

A ridiculously trivial claim.  You really need to take care with your
language.


You are a master of deception of avoiding the point:

I am just pointing out you need to say what you mean.  Having an x86
emulator that aborts infinite loops and infinite recursion is trivial
and (I hope) not what you think you have.

Having an equivalent computation to the {Linz, Sipser} H correctly
deciding the Linz Ĥ, the Sipser D and the Kozen N is what I have.

Which you will be (finally) posting today?


I just finished the programming of this.
I wanted to get it complete on the anniversary of its creation.

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Mon, 14 Dec 2020 14:25 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <FYednaMDdu1C0knCnZ2dnUU7-fPNnZ2d@giganews.com> <rr1keo$3je$1@dont-email.me> <oJednefmb72Gy0nCnZ2dnUU7-UPNnZ2d@giganews.com> <rr1lhm$8ul$1@dont-email.me> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com> <rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com> <rr2vb1$mhs$1@dont-email.me> <SrSdnbIYprUrnEjCnZ2dnUU7-U2dnZ2d@giganews.com> <rr30u4$2ba$1@dont-email.me> <BcSdnZTygJfElkjCnZ2dnUU7-UednZ2d@giganews.com> <rr340r$l9i$1@dont-email.me> <bo2dnRdK_KDeiEjCnZ2dnUU7-UnNnZ2d@giganews.com> <rr34ok$rof$1@dont-email.me> <oaedncLQ-96MhEjCnZ2dnUU7-WnNnZ2d@giganews.com> <rr36c2$7dk$1@dont-email.me> <-LCdnQjCJqk1vEjCnZ2dnUU7-eXNnZ2d@giganews.com> <rr39me$tev$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 14 Dec 2020 08:25:56 -0600
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On 12/12/2020 2:37 PM, André G. Isaak wrote:
On 2020-12-12 13:01, olcott wrote:
On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly beyond me.

I am saying that anything which has the possibility of getting caught in infinite recursion cannot return a result and therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect infinite recursion on itself and return its decision to its caller does not count.

Basically you are saying that it is wrong all of the time even though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return a result for *all* inputs. That's the definition of 'decider'. Something that only returns results in some instances is not a decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly decide that it has been infinitely invoked that even though this decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for other inputs, then this same idea can be extended to some invocations and not all invocations, otherwise correctly deciding infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a dollar. A partial decider is something that correctly decides some cases, not something which is a decider in some cases. Things are either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen} counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a decider in those cases. You could call it a partial decider, but not a decider.

However, in the case of your program, you can't even call it that because it sometimes returns and other times does not return *on the same input*. A partial decider is something which decides some set of inputs and fails to decide another, *disjoint* set of inputs. Something which gets different results for the same input isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that it has been invoked in infinite recursion it must fix the bug in this infinitely recursive invocation so that it can report its infinitely recursive invocation to its infinitely recursive caller, that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>

No, I did not say that. You need to make at least some effort to read for comprehension. I said that something which can be caught in infinite recursion is *not* a decider. This is getting rather tedious. Something that correctly decides some cases but not others could be a partial decider, but not if it decides the *same* input in some cases but not others.


01 void H_Hat(u32 P)
02 {
03   u32 Input_Halts = DebugTrace(P, P);
04   if (Input_Halts)
05     HERE: goto HERE;
06   else
07     HALT
08 }

Halts((u32)H_Hat,(u32)H_Hat) is correctly decided** as not halting because it aborts the invocation of itself on line 03.

** Halts returns the correct halting determination.

According to your way of defining a decider:
(a) Halts is not a decider even though it correctly decides.
(b) Halts would be a decider if it aborted the infinite recursion of any other function besides itself.

That is ridiculous!


Just to be very clear here, the term "partial decider" does not denote a type of decider; it denotes something which decides some cases but not others. A "decider" denotes something which decides all cases. They are different things.

Also, note that the infinite recursion is caused by the way you've designed Halts(), not by some bug present in its caller. You're making it sound like if it is given input that leads to infinite recursion this is because the caller did something wrong. That's simply not the case. It's because your "decider" is broken.

André



--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.lang.c, comp.lang.c++
Followup: comp.theory
Date: Mon, 14 Dec 2020 15:16 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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NNTP-Posting-Date: Mon, 14 Dec 2020 09:16:05 -0600
Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within
infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.lang.c,comp.lang.c++
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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From: NoO...@NoWhere.com (olcott)
Followup-To: comp.theory
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On 12/14/2020 8:48 AM, André G. Isaak wrote:
On 2020-12-14 07:25, olcott wrote:
On 12/12/2020 2:37 PM, André G. Isaak wrote:
On 2020-12-12 13:01, olcott wrote:
On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly beyond me.

I am saying that anything which has the possibility of getting caught in infinite recursion cannot return a result and therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect infinite recursion on itself and return its decision to its caller does not count.

Basically you are saying that it is wrong all of the time even though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return a result for *all* inputs. That's the definition of 'decider'. Something that only returns results in some instances is not a decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly decide that it has been infinitely invoked that even though this decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for other inputs, then this same idea can be extended to some invocations and not all invocations, otherwise correctly deciding infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a dollar. A partial decider is something that correctly decides some cases, not something which is a decider in some cases. Things are either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen} counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a decider in those cases. You could call it a partial decider, but not a decider.

However, in the case of your program, you can't even call it that because it sometimes returns and other times does not return *on the same input*. A partial decider is something which decides some set of inputs and fails to decide another, *disjoint* set of inputs. Something which gets different results for the same input isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that it has been invoked in infinite recursion it must fix the bug in this infinitely recursive invocation so that it can report its infinitely recursive invocation to its infinitely recursive caller, that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>

No, I did not say that. You need to make at least some effort to read for comprehension. I said that something which can be caught in infinite recursion is *not* a decider. This is getting rather tedious. Something that correctly decides some cases but not others could be a partial decider, but not if it decides the *same* input in some cases but not others.


01 void H_Hat(u32 P)
02 {
03   u32 Input_Halts = DebugTrace(P, P);
04   if (Input_Halts)
05     HERE: goto HERE;
06   else
07     HALT
08 }

Halts((u32)H_Hat,(u32)H_Hat) is correctly decided** as not halting because it aborts the invocation of itself on line 03.

You've switched back from using Halts() to using DebugTrace(). Are these intended to be distinct functions?

** Halts returns the correct halting determination.

According to your way of defining a decider:
(a) Halts is not a decider even though it correctly decides.
(b) Halts would be a decider if it aborted the infinite recursion of any other function besides itself.

That is ridiculous!
Look, a decider is a type of *function*. To be a function, something must consistently map the same input to the same result, but that isn't what you get above. Assuming that your DebugTrace() and Halts() are intended to be the same, you are claiming that

Halts(H_Hat, H_Hat)

returns false. This means Halts(H_Hat, H_Hat) is a finite computation.

But by returning false is is also claiming that the instance of Halts(H_Hat, H_Hat) invoked from within H_Hat must be aborted as a non-halting function.

This is a contradiction.

As I have said very many times (no one notices because they only glance at a few of my words to contrive some lame basis for a rebuttal that would fool the gullible):

Halts(H_Hat, H_Hat) is only a finite computation because it aborts the otherwise infinite recursion of its input according to this criteria:

On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
 > A computation that would not halt if its simulation were not
 > halted is indeed a non-halting computation.

On Saturday, November 28, 2020 at 2:00:28 PM UTC-8, olcott wrote:
 > Every computation that would not halt if its simulation
 > were not halted is by logical necessity a non-halting computation.

Either Halts(H_Hat, H_Hat) is finite or it isn't. It can't be finite in one case and non-finite in the other given that it is the same function with the same input.

André



--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite recursion)
From: Kaz Kylheku
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Followup: comp.theory
Organization: Aioe.org NNTP Server
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From: 563-365-...@kylheku.com (Kaz Kylheku)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
Subject: Re: Refuting the Peter Linz HP Proof (deciders within infinite
recursion)
Followup-To: comp.theory
Date: Mon, 14 Dec 2020 17:45:51 +0000 (UTC)
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On 2020-12-14, olcott <NoOne@NoWhere.com> wrote:
01 void H_Hat(u32 P)
02 {
03   u32 Input_Halts = DebugTrace(P, P);
04   if (Input_Halts)
05     HERE: goto HERE;
06   else
07     HALT
08 }

Halts((u32)H_Hat,(u32)H_Hat) is correctly decided** as not halting
because it aborts the invocation of itself on line 03.

Halts can decide whether the above function halts on itself because
that function doesn't call Halts. That function calls something
called DebugTrace, and so its purpose is to show that DebugTrace
is not a universal halting decider.

To show that, we need a main() which looks like this:

  int main(void)
  {
    u32 Input_Halts = DebugTrace(H_Hat, H_Hat);
    if (Input_Halts)
      puts("DebugTrace says H_Hat(H_Hat) halts")
    else
      puts("DebugTrace says H_Hat(H_Hat) fails to halt")
    return 0;
  }

The original Halts, and a debug-traced version of Halts, are not the
same computation. The source code of Halts may be the same, and even
the machine code, but the two are not executed according to the same
execution model.

If one execution model breaks an infinite loop, and somehow sweeps that
fact under the rug so that the function returns normally, so that the
function is deemed to have halted, that is intellectually dishonest at
best, and stupid at worst.


Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.lang.c, comp.lang.c++
Followup: comp.theory
Date: Mon, 14 Dec 2020 18:41 UTC
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NNTP-Posting-Date: Mon, 14 Dec 2020 12:42:21 -0600
Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within
infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.lang.c,comp.lang.c++
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com>
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<7fbe5f35-e17b-4964-888d-ef038a6a2126n@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Followup-To: comp.theory
Date: Mon, 14 Dec 2020 12:41:56 -0600
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On 12/14/2020 9:32 AM, Malcolm McLean wrote:
On Monday, 14 December 2020 at 15:16:13 UTC, olcott wrote:
On 12/14/2020 8:48 AM, André G. Isaak wrote:
On 2020-12-14 07:25, olcott wrote:
On 12/12/2020 2:37 PM, André G. Isaak wrote:
On 2020-12-12 13:01, olcott wrote:
On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its
caller even though it must sometimes abort the
simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner
instances and to abort those instances only in cases
where they would not otherwise halt, it is asserting that
there *are* inputs to Halts() which will not halt. Ergo,
it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a
value to its caller Halts() is not a decider. On those
invocations of Halts() where it does halt and return a
value to its caller it is a decider.

A program is either a decider or it isn't. There's no such
thing as a program which is sometimes a decider and
sometimes isn't.

André


You already know that is pure bullshit or the term "partial
decider" would not exist. What motive do you have for saying
things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is
not a "sometimes decider".

A partial decider makes a correct decision for a particular
class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the
*same* inputs. So you cannot even claim your program is a
partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some
infinitely recursive invocations <do> return a result to their
caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly
beyond me.

I am saying that anything which has the possibility of getting
caught in infinite recursion cannot return a result and
therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite
recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect
infinite recursion on itself and return its decision to its
caller does not count.

Basically you are saying that it is wrong all of the time even
though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return
a result for *all* inputs. That's the definition of 'decider'.
Something that only returns results in some instances is not a
decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly
decide that it has been infinitely invoked that even though this
decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for
other inputs, then this same idea can be extended to some
invocations and not all invocations, otherwise correctly deciding
infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a
dollar. A partial decider is something that correctly decides some
cases, not something which is a decider in some cases. Things are
either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen}
counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a
decider in those cases. You could call it a partial decider, but
not a decider.

However, in the case of your program, you can't even call it that
because it sometimes returns and other times does not return *on
the same input*. A partial decider is something which decides some
set of inputs and fails to decide another, *disjoint* set of
inputs. Something which gets different results for the same input
isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that
it has been invoked in infinite recursion it must fix the bug in
this infinitely recursive invocation so that it can report its
infinitely recursive invocation to its infinitely recursive caller,
that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>

No, I did not say that. You need to make at least some effort to read
for comprehension. I said that something which can be caught in
infinite recursion is *not* a decider. This is getting rather
tedious. Something that correctly decides some cases but not others
could be a partial decider, but not if it decides the *same* input in
some cases but not others.


01 void H_Hat(u32 P)
02 {
03 u32 Input_Halts = DebugTrace(P, P);
04 if (Input_Halts)
05 HERE: goto HERE;
06 else
07 HALT
08 }

Halts((u32)H_Hat,(u32)H_Hat) is correctly decided** as not halting
because it aborts the invocation of itself on line 03.

You've switched back from using Halts() to using DebugTrace(). Are these
intended to be distinct functions?

** Halts returns the correct halting determination.

According to your way of defining a decider:
(a) Halts is not a decider even though it correctly decides.
(b) Halts would be a decider if it aborted the infinite recursion of
any other function besides itself.

That is ridiculous!
Look, a decider is a type of *function*. To be a function, something
must consistently map the same input to the same result, but that isn't
what you get above. Assuming that your DebugTrace() and Halts() are
intended to be the same, you are claiming that

Halts(H_Hat, H_Hat)

returns false. This means Halts(H_Hat, H_Hat) is a finite computation.

But by returning false is is also claiming that the instance of
Halts(H_Hat, H_Hat) invoked from within H_Hat must be aborted as a
non-halting function.

This is a contradiction.
As I have said very many times (no one notices because they only glance
at a few of my words to contrive some lame basis for a rebuttal that
would fool the gullible):

Halts(H_Hat, H_Hat) is only a finite computation because it aborts the
otherwise infinite recursion of its input according to this criteria:

On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
A computation that would not halt if its simulation were not
halted is indeed a non-halting computation.

If Halts aborts itself, is it halted or aborted? That's the question.


Halts() simulates H_Hat() that invokes Halts() in infinite recursion.
Halts() stops simulating H_Hat() including its infinite recursive invocation of Halts(), returning its non-halting decision to main() where it is output.

If we say "halted" then H_Hat inverts whatever result it returns,

It is not possible for an aborted function to invert any damn thing.

and :Halts" is wrong. If we say "aborted" then "Halts" isn't a function,
which is a slightly more subtle requirement of H_Hat.

Certainly an at least partial halt decider that bases its halting decision by looking for patterns of behavior of its inputs can stop simulating this input as soon as it detects any non-halting pattern.

It does not make any damn difference if it detects an infinite loop, or infinite recursion. It also does not make any damn difference which function is involved in infinite recursion. As long as Halts() detects the non-halting behavior of its input then it can stop simulating this input and report non-halting.

void H_Hat(u32 P)
{
   u32 Input_Halts = Halts(P, P);
   if (Input_Halts)
     HERE: goto HERE;
   else
     HALT
}


int main()
{
   u32 Input_Would_Halt = Halts((u32)H_Hat, (u32)H_Hat);
   Output("[Input_Would_Halt] =", Input_Would_Halt);
   HALT;
}

I finally renamed my internal DebugTrace() to Halts() now that it finally does return its correct halting decision to main().

--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within infinite recursion)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, comp.software-eng
Date: Mon, 14 Dec 2020 18:50 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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NNTP-Posting-Date: Mon, 14 Dec 2020 12:50:08 -0600
Subject: Re: Refuting the {Linz, Sipser and Kozen} HP Proofs (deciders within infinite recursion)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng
References: <3JSdnRrpiNHInV3CnZ2dnUU7-YHNnZ2d@giganews.com> <YpmdndEqq_dqV0nCnZ2dnUU7-Y2dnZ2d@giganews.com> <rr2i8o$tee$1@dont-email.me> <EK-dnYNCHMf7UEnCnZ2dnUU7-UGdnZ2d@giganews.com> <rr2j08$4ur$1@dont-email.me> <0KadnafWuKP6f0nCnZ2dnUU7-IPNnZ2d@giganews.com> <rr2oq2$ao3$1@dont-email.me> <35OdnezHsPxac0nCnZ2dnUU7-YvNnZ2d@giganews.com> <rr2tlk$c32$1@dont-email.me> <zp6dnf8CEZuHnUjCnZ2dnUU7-SfNnZ2d@giganews.com> <rr2vb1$mhs$1@dont-email.me> <SrSdnbIYprUrnEjCnZ2dnUU7-U2dnZ2d@giganews.com> <rr30u4$2ba$1@dont-email.me> <BcSdnZTygJfElkjCnZ2dnUU7-UednZ2d@giganews.com> <rr340r$l9i$1@dont-email.me> <bo2dnRdK_KDeiEjCnZ2dnUU7-UnNnZ2d@giganews.com> <rr34ok$rof$1@dont-email.me> <oaedncLQ-96MhEjCnZ2dnUU7-WnNnZ2d@giganews.com> <rr36c2$7dk$1@dont-email.me> <-LCdnQjCJqk1vEjCnZ2dnUU7-eXNnZ2d@giganews.com> <rr39me$tev$1@dont-email.me> <IdGdnS9EruNl6ErCnZ2dnUU7-QvNnZ2d@giganews.com> <rr7tvl$h7a$1@dont-email.me> <DLCdnTdFDrYoHErCnZ2dnUU7-e3NnZ2d@giganews.com> <rr80h6$5t9$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 14 Dec 2020 12:50:05 -0600
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On 12/14/2020 9:31 AM, André G. Isaak wrote:
On 2020-12-14 08:16, olcott wrote:
On 12/14/2020 8:48 AM, André G. Isaak wrote:
On 2020-12-14 07:25, olcott wrote:
On 12/12/2020 2:37 PM, André G. Isaak wrote:
On 2020-12-12 13:01, olcott wrote:
On 12/12/2020 1:40 PM, André G. Isaak wrote:
On 2020-12-12 12:25, olcott wrote:
On 12/12/2020 1:13 PM, André G. Isaak wrote:
On 2020-12-12 12:08, olcott wrote:
On 12/12/2020 1:00 PM, André G. Isaak wrote:
On 2020-12-12 11:26, olcott wrote:
On 12/12/2020 12:08 PM, André G. Isaak wrote:
On 2020-12-12 10:45, olcott wrote:
On 12/12/2020 11:40 AM, André G. Isaak wrote:
On 2020-12-12 10:38, olcott wrote:
On 12/12/2020 11:12 AM, André G. Isaak wrote:
On 2020-12-12 09:24, olcott wrote:

<snip>

The outermost Halts() always returns a value to its caller even though it must sometimes abort the simulations of inner infinite invocations of itself.

And since it claims to be simulating those inner instances and to abort those instances only in cases where they would not otherwise halt, it is asserting that there *are* inputs to Halts() which will not halt. Ergo, it is asserting that Halts() is *not* a decider.

...in those cases where it does not halt and return a value to its caller Halts() is not a decider. On those invocations of Halts() where it does halt and return a value to its caller it is a decider.

A program is either a decider or it isn't. There's no such thing as a program which is sometimes a decider and sometimes isn't.

André


You already know that is pure bullshit or the term "partial decider" would not exist. What motive do you have for saying things that you know are pure bullshit?

A partial decider is not a decider. More importantly, it is not a "sometimes decider".

A partial decider makes a correct decision for a particular class of inputs but may fail to halt for other inputs.


Your program sometimes halts and sometimes doesn't for the *same* inputs. So you cannot even claim your program is a partial decider, let alone an actual decider.

André


So in other words you "believe" against logic that some infinitely recursive invocations <do> return a result to their caller. That sounds nutty to me.

How you can possibly get that idea from what I wrote is utterly beyond me.

I am saying that anything which has the possibility of getting caught in infinite recursion cannot return a result and therefore cannot constitute a decider.

André



Except in those cases that it has not been caught in infinite recursion and does return a result to its caller.

Alternatively a function that can and does correctly detect infinite recursion on itself and return its decision to its caller does not count.

Basically you are saying that it is wrong all of the time even though it is right some of the time.

No. I am saying that it is not a decider. A decider *must* return a result for *all* inputs. That's the definition of 'decider'. Something that only returns results in some instances is not a decider. I don't know how I can make this any clearer...

André


The way that you are defining it when a function does correctly decide that it has been infinitely invoked that even though this decision is correct it does not count.

Since a partial decider <is> a decider for some inputs and not for other inputs, then this same idea can be extended to some invocations and not all invocations, otherwise correctly deciding infinite recursion does not count even when the decision is correct.

A partial decider is not a decider any more than a half-dollar is a dollar. A partial decider is something that correctly decides some cases, not something which is a decider in some cases. Things are either deciders or they aren't.

A partial decider that decides the {Linz, Sipser, Kozen} counter-examples refutes these three proofs.

That a program correctly decides some cases does not make it a decider in those cases. You could call it a partial decider, but not a decider.

However, in the case of your program, you can't even call it that because it sometimes returns and other times does not return *on the same input*. A partial decider is something which decides some set of inputs and fails to decide another, *disjoint* set of inputs. Something which gets different results for the same input isn't even a function, let alone a decider or partial decider.

André


So in other words when a partial decider correctly determines that it has been invoked in infinite recursion it must fix the bug in this infinitely recursive invocation so that it can report its infinitely recursive invocation to its infinitely recursive caller, that is no longer infinitely recursive because it fixed this bug.

<sarcasm>
That makes perfect sense to me.
</sarcasm>

No, I did not say that. You need to make at least some effort to read for comprehension. I said that something which can be caught in infinite recursion is *not* a decider. This is getting rather tedious. Something that correctly decides some cases but not others could be a partial decider, but not if it decides the *same* input in some cases but not others.


01 void H_Hat(u32 P)
02 {
03   u32 Input_Halts = DebugTrace(P, P);
04   if (Input_Halts)
05     HERE: goto HERE;
06   else
07     HALT
08 }

Halts((u32)H_Hat,(u32)H_Hat) is correctly decided** as not halting because it aborts the invocation of itself on line 03.

You've switched back from using Halts() to using DebugTrace(). Are these intended to be distinct functions?

** Halts returns the correct halting determination.

According to your way of defining a decider:
(a) Halts is not a decider even though it correctly decides.
(b) Halts would be a decider if it aborted the infinite recursion of any other function besides itself.

That is ridiculous!
Look, a decider is a type of *function*. To be a function, something must consistently map the same input to the same result, but that isn't what you get above. Assuming that your DebugTrace() and Halts() are intended to be the same, you are claiming that

Halts(H_Hat, H_Hat)

returns false. This means Halts(H_Hat, H_Hat) is a finite computation.

But by returning false is is also claiming that the instance of Halts(H_Hat, H_Hat) invoked from within H_Hat must be aborted as a non-halting function.

This is a contradiction.

As I have said very many times (no one notices because they only glance at a few of my words to contrive some lame basis for a rebuttal that would fool the gullible):

Halts(H_Hat, H_Hat) is only a finite computation because it aborts the otherwise infinite recursion of its input according to this criteria:

And the Halts(H_Hat, H_Hat) called from within H_Hat should be a finite computation for the exact same reason. It has the exact same ability to abort its input as your outermost call to Halts() has.

If you were to run H_Hat(H_Hat) as an independent program, then it's call to Halts(H_Hat, H_Hat) would behave in exactly the same way as the call to Halts(H_Hat, H_Hat) described above.

In my halt deciding solution it is impossible to run anything as an independent program, everything is simulated so that nothing can be done behind the back of the halt decider.


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Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre minds." Einstein


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