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devel / comp.theory / Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

SubjectAuthor
* H(P,P)==0 is correct for every simulating halt decider H --- V2olcott
+* H(P,P)==0 is correct for every simulating halt decider H --- V2Ben Bacarisse
|`* H(P,P)==0 is correct for every simulating halt decider H --- V2olcott
| +* H(P,P)==0 is correct for every simulating halt decider H --- V2Ben Bacarisse
| |`* H(P,P)==0 is correct for every simulating halt decider H --- V2olcott
| | +- H(P,P)==0 is correct for every simulating halt decider H --- V2Richard Damon
| | `* H(P,P)==0 is correct for every simulating halt decider H --- V2Ben Bacarisse
| |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2olcott
| |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2Ben Bacarisse
| |   |+* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versolcott
| |   ||`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   || `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   ||  |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versolcott
| |   ||  | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incolcott
| |   ||  | | | | | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | | `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incolcott
| |   ||  | | | | |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |   |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |   | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |   | | |+* H(P,P)==0 is correct for every simulating halt decider H --- V2 [Mike Terry
| |   ||  | | | | |   | | ||+* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | |||`- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | | ||`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [Mike Terry
| |   ||  | | | | |   | | || +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | || |`- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | | || `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | |+* H(P,P)==0 is correct for every simulating halt decider H --- V2 [Malcolm McLean
| |   ||  | | | | |   | | ||`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | || `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | | `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |   | | |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  | | | | |   | | |   |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  | | | | |   | | |   | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | | |   `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | |   `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  | `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   ||  |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterBen Bacarisse
| |   ||  |   | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterBen Bacarisse
| |   ||  |   | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | | |+* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | | ||`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | | || `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | | ||  +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | | ||  |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | | | ||  | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | | ||  | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ complete proofolcott
| |   ||  |   | | | ||  | | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | | ||  | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | | | ||  | `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | | ||  |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ complete proofolcott
| |   ||  |   | | | ||  |   `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | | ||  `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | | |`- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterBen Bacarisse
| |   ||  |   |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   ||  |   | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   ||  |   | +- H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterBen Bacarisse
| |   ||  |   | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  |   `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   ||  `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   | +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   | |`* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   | | `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   | |  `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   | |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versBen Bacarisse
| |   | |   |`- H(P,P)==0 is correct for every simulating halt decider H --- V2 [olcott
| |   | |   `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   | |    `* H(P,P)==0 is correct for every simulating halt decider H --- V2 [André G. Isaak
| |   | |     `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   | `- H(P,P)==0 is correct for every simulating halt decider H --- V2 [Richard Damon
| |   +* H(P,P)==0 is correct for every simulating halt decider H --- V2André G. Isaak
| |   `- H(P,P)==0 is correct for every simulating halt decider H --- V2Richard Damon
| `- H(P,P)==0 is correct for every simulating halt decider H --- V2Richard Damon
+- H(P,P)==0 is correct for every simulating halt decider H --- V2Richard Damon
`* H(P,P)==0 is correct for every simulating halt decider H --- V2Malcolm McLean

Pages:123456
Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

<pqadnbWVhZbfPB_8nZ2dnUU7-YmdnZ2d@giganews.com>

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https://www.novabbs.com/devel/article-flat.php?id=22946&group=comp.theory#22946

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
impossibly incorrect ]
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 by: olcott - Wed, 3 Nov 2021 14:48 UTC

On 11/2/2021 10:30 PM, André G. Isaak wrote:
> On 2021-11-02 21:14, olcott wrote:
>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>> On 2021-11-02 19:32, olcott wrote:
>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>
>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when it
>>>>>>>>>>>> correctly reports what the actual behavior of its actual
>>>>>>>>>>>> input would be then everyone (besides me) is wrong.
>>>>>>>>>>>
>>>>>>>>>>> The definition tells you what a halt decider *is*. It doesn't
>>>>>>>>>>> define it as 'wrong'. It defines what question it is supposed
>>>>>>>>>>> to answer.
>>>>>>>>>>>
>>>>>>>>>>> The input to a halt decider is a string. Strings don't *have*
>>>>>>>>>>> halting behaviour so your position above is entirely incoherent.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> In computability theory, the halting problem is the problem of
>>>>>>>>>> determining, from a description of an arbitrary computer
>>>>>>>>>> program and an input, whether the program will finish running,
>>>>>>>>>> or continue to run forever.
>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>
>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>
>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>> 'simulations' just as the more formal definition used by Linz's
>>>>>>>>> does not.
>>>>>>>>>
>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>> simulation of its input would ever reach a final state of this
>>>>>>>>>> input by a simulating halt decider.
>>>>>>>>>
>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>> identically to the actual TM being simulated. That means that
>>>>>>>>> if the actual TM halts the simulation also must halt. Which
>>>>>>>>> means that your simulation is not a 'correct simulation'.
>>>>>>>>>
>>>>>>>>
>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>> simulation is correct.
>>>>>>>
>>>>>>> I have no idea what it means for a simulation of P(P) to "match
>>>>>>> its x86 source code".
>>>>>>>
>>>>>>
>>>>>> When the simulator executes the instructions at
>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>> of the x86 source code of P, then the simulator
>>>>>> correctly simulated P(P).
>>>>>
>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>> accurately duplicates *all* of the behaviour of that machine. Part
>>>>> of the behaviour of P(P) is that it halts.
>>>>>
>>>>
>>>> That is a stupid thing to say. The x86 emulator correctly emulates
>>>> the x86 instructions of P iff it emulates the actual x86 intructions
>>>> of P saying anything else is both pure bullshit and quite nutty.
>>>
>>> That's a nonsensical claim. If it correctly emulates all the
>>> instructions then it should have identical behaviour. That includes
>>> whether it halts or not.
>>
>> Maybe you don't understand the x86 language well enough to ever
>> understand what I am saying.
>>
>> While H continues to simulate P these first seven instructions of P
>> continue to repeat. Do you understand that?
>
> Which is irrelevant to the halting problem

I will not speak with you until you answer.

> which asks whether P(P)
> halts? Does it? Yes. Ergo the only correct for H(P, P) to give is
> 'true'. *Nothing* apart from the actual behaviour of P(P) is relevant to
> determining what the correct answer to this question is, so there's not
> even any point in providing all your meaningless traces.
>
> The correct answer to H(P, P) is determined by the actual behaviour of
> P(P). We know the actual behaviour of P(P). So there's absolutely no
> reason to consider anything else.
>
> And you conveniently ignored all the questions which I asked.

Because they were all based on false assumptions that
I can correct only if you answer my questions.

>
> What does the input to H(P, P) represent if not P(P)?
>
> How can the inputs to H1(P, P) and H(P, P) represent different things
> given that they are the *same* input?
>
> André
>
>

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

<slu7qp$16qj$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=22947&group=comp.theory#22947

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From: news.dea...@darjeeling.plus.com (Mike Terry)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
impossibly incorrect ]
Date: Wed, 3 Nov 2021 14:54:17 +0000
Organization: Aioe.org NNTP Server
Message-ID: <slu7qp$16qj$1@gioia.aioe.org>
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 by: Mike Terry - Wed, 3 Nov 2021 14:54 UTC

On 03/11/2021 04:09, Mike Terry wrote:
> On 03/11/2021 03:30, André G. Isaak wrote:
>> On 2021-11-02 21:14, olcott wrote:
>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>> On 2021-11-02 19:32, olcott wrote:
>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when
>>>>>>>>>>>>> it correctly reports what the actual behavior of its actual
>>>>>>>>>>>>> input would be then everyone (besides me) is wrong.
>>>>>>>>>>>>
>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it is
>>>>>>>>>>>> supposed to answer.
>>>>>>>>>>>>
>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>> *have* halting behaviour so your position above is entirely
>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>>>> running, or continue to run forever.
>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>
>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>
>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>> Linz's does not.
>>>>>>>>>>
>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>
>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>> identically to the actual TM being simulated. That means that
>>>>>>>>>> if the actual TM halts the simulation also must halt. Which
>>>>>>>>>> means that your simulation is not a 'correct simulation'.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>> simulation is correct.
>>>>>>>>
>>>>>>>> I have no idea what it means for a simulation of P(P) to "match
>>>>>>>> its x86 source code".
>>>>>>>>
>>>>>>>
>>>>>>> When the simulator executes the instructions at
>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>> of the x86 source code of P, then the simulator
>>>>>>> correctly simulated P(P).
>>>>>>
>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>> accurately duplicates *all* of the behaviour of that machine. Part
>>>>>> of the behaviour of P(P) is that it halts.
>>>>>>
>>>>>
>>>>> That is a stupid thing to say. The x86 emulator correctly emulates
>>>>> the x86 instructions of P iff it emulates the actual x86
>>>>> intructions of P saying anything else is both pure bullshit and
>>>>> quite nutty.
>>>>
>>>> That's a nonsensical claim. If it correctly emulates all the
>>>> instructions then it should have identical behaviour. That includes
>>>> whether it halts or not.
>>>
>>> Maybe you don't understand the x86 language well enough to ever
>>> understand what I am saying.
>>>
>>> While H continues to simulate P these first seven instructions of P
>>> continue to repeat. Do you understand that?
>>
>> Which is irrelevant to the halting problem which asks whether P(P)
>> halts? Does it? Yes. Ergo the only correct for H(P, P) to give is
>> 'true'. *Nothing* apart from the actual behaviour of P(P) is relevant
>> to determining what the correct answer to this question is, so there's
>> not even any point in providing all your meaningless traces.
>>
>> The correct answer to H(P, P) is determined by the actual behaviour of
>> P(P). We know the actual behaviour of P(P). So there's absolutely no
>> reason to consider anything else.
>>
>> And you conveniently ignored all the questions which I asked.
>>
>> What does the input to H(P, P) represent if not P(P)?
>>
>> How can the inputs to H1(P, P) and H(P, P) represent different things
>> given that they are the *same* input?
>
> My suspicion (difficult to confirm) is still that in both those cases,
> PO is looking at the same computation.  It's simply that H and H1, in
> examining the identical execution traces, behave differently because
> they take their own machine code address and use that in interpreting
> the instruction trace.
>
> So e.g. H uses its address to exclude certain parts of the trace it
> examines, and consequently INCORRECTLY decides it is seeing infinite
> recursion.  H1 excludes a different address range, so it doesn't see
> infinite recursion and so the simulation continues FURTHER than H
> continues it, and in fact with H1 the simulation proceeds right up to
> the point where it reaches its halt state, so H1 give the correct
> answer.  [I'd guess H1 works because it is seeing the conditional branch
> instructions that H deliberately ignores, and so his unsound recursion
> test does not match.]
>
> I bet if we looked at the actual traces that H and H1 are producing,

Correction - what I meant to say here is "actual traces that H and H1
are EXAMINING".

Obviously the traces of H(P,P) and H1(P,P) [including the traces of the
outer emulations of H, H1 themselves] will be different, because H and
H1 addresses will be different if nothing else.

That's a trivial point, but seems to be a constant point of
miscomunication between PO and others. I reckon that when PO says
"computations H(P,P) and H1(P,P)" he is intending to say "the traces of
the SIMULATIONS of P(P) within H and H1", or similar. [And if I'm right
above, those are NOT different, other than that H1 simulates FURTHER
than H, and so gets to observe the simulation halting. Nothing to do
with the presence of mysterious PSR!.]

Mike.

> they would be exactly the same UP TO THE POINT WHERE H MAKES ITS MISTAKE
> AND SAYS "INFINITE RECURSION DETECTED".  I.e. H just makes the wrong
> decision and terminates the simulation too early, like everyone has been
> saying for over a year...  :)
>
> Mike.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

<3JWdnce5TrR1Nh_8nZ2dnUU7-bnNnZ2d@giganews.com>

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
impossibly incorrect ]
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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Wed, 3 Nov 2021 15:34 UTC

On 11/3/2021 9:54 AM, Mike Terry wrote:
> On 03/11/2021 04:09, Mike Terry wrote:
>> On 03/11/2021 03:30, André G. Isaak wrote:
>>> On 2021-11-02 21:14, olcott wrote:
>>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>>> On 2021-11-02 19:32, olcott wrote:
>>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when
>>>>>>>>>>>>>> it correctly reports what the actual behavior of its
>>>>>>>>>>>>>> actual input would be then everyone (besides me) is wrong.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it
>>>>>>>>>>>>> is supposed to answer.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>>> *have* halting behaviour so your position above is entirely
>>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>>>>> running, or continue to run forever.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>
>>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>>
>>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>>> Linz's does not.
>>>>>>>>>>>
>>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>>
>>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>>> identically to the actual TM being simulated. That means that
>>>>>>>>>>> if the actual TM halts the simulation also must halt. Which
>>>>>>>>>>> means that your simulation is not a 'correct simulation'.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>>> simulation is correct.
>>>>>>>>>
>>>>>>>>> I have no idea what it means for a simulation of P(P) to "match
>>>>>>>>> its x86 source code".
>>>>>>>>>
>>>>>>>>
>>>>>>>> When the simulator executes the instructions at
>>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>>> of the x86 source code of P, then the simulator
>>>>>>>> correctly simulated P(P).
>>>>>>>
>>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>>> accurately duplicates *all* of the behaviour of that machine.
>>>>>>> Part of the behaviour of P(P) is that it halts.
>>>>>>>
>>>>>>
>>>>>> That is a stupid thing to say. The x86 emulator correctly emulates
>>>>>> the x86 instructions of P iff it emulates the actual x86
>>>>>> intructions of P saying anything else is both pure bullshit and
>>>>>> quite nutty.
>>>>>
>>>>> That's a nonsensical claim. If it correctly emulates all the
>>>>> instructions then it should have identical behaviour. That includes
>>>>> whether it halts or not.
>>>>
>>>> Maybe you don't understand the x86 language well enough to ever
>>>> understand what I am saying.
>>>>
>>>> While H continues to simulate P these first seven instructions of P
>>>> continue to repeat. Do you understand that?
>>>
>>> Which is irrelevant to the halting problem which asks whether P(P)
>>> halts? Does it? Yes. Ergo the only correct for H(P, P) to give is
>>> 'true'. *Nothing* apart from the actual behaviour of P(P) is relevant
>>> to determining what the correct answer to this question is, so
>>> there's not even any point in providing all your meaningless traces.
>>>
>>> The correct answer to H(P, P) is determined by the actual behaviour
>>> of P(P). We know the actual behaviour of P(P). So there's absolutely
>>> no reason to consider anything else.
>>>
>>> And you conveniently ignored all the questions which I asked.
>>>
>>> What does the input to H(P, P) represent if not P(P)?
>>>
>>> How can the inputs to H1(P, P) and H(P, P) represent different things
>>> given that they are the *same* input?
>>
>> My suspicion (difficult to confirm) is still that in both those cases,
>> PO is looking at the same computation.  It's simply that H and H1, in
>> examining the identical execution traces, behave differently because
>> they take their own machine code address and use that in interpreting
>> the instruction trace.
>>
>> So e.g. H uses its address to exclude certain parts of the trace it
>> examines, and consequently INCORRECTLY decides it is seeing infinite
>> recursion.  H1 excludes a different address range, so it doesn't see
>> infinite recursion and so the simulation continues FURTHER than H
>> continues it, and in fact with H1 the simulation proceeds right up to
>> the point where it reaches its halt state, so H1 give the correct
>> answer.  [I'd guess H1 works because it is seeing the conditional
>> branch instructions that H deliberately ignores, and so his unsound
>> recursion test does not match.]
>>
>> I bet if we looked at the actual traces that H and H1 are producing,
>
> Correction - what I meant to say here is "actual traces that H and H1
> are EXAMINING".
>
> Obviously the traces of H(P,P) and H1(P,P) [including the traces of the
> outer emulations of H, H1 themselves] will be different, because H and
> H1 addresses will be different if nothing else.
>
> That's a trivial point, but seems to be a constant point of
> miscomunication between PO and others.  I reckon that when PO says
> "computations H(P,P) and H1(P,P)" he is intending to say "the traces of
> the SIMULATIONS of P(P) within H and H1", or similar.  [And if I'm right
> above, those are NOT different, other than that H1 simulates FURTHER
> than H, and so gets to observe the simulation halting.  Nothing to do
> with the presence of mysterious PSR!.]
>
> Mike.
>

_P()
[00000c36](01) 55 push ebp
[00000c37](02) 8bec mov ebp,esp
[00000c39](03) 8b4508 mov eax,[ebp+08] // 2nd Param
[00000c3c](01) 50 push eax
[00000c3d](03) 8b4d08 mov ecx,[ebp+08] // 1st Param
[00000c40](01) 51 push ecx
[00000c41](05) e820fdffff call 00000966 // call H
[00000c46](03) 83c408 add esp,+08
[00000c49](02) 85c0 test eax,eax
[00000c4b](02) 7402 jz 00000c4f
[00000c4d](02) ebfe jmp 00000c4d
[00000c4f](01) 5d pop ebp
[00000c50](01) c3 ret
Size in bytes:(0027) [00000c50]


Click here to read the complete article
Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

<sluaa3$jaa$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
impossibly incorrect ]
Date: Wed, 3 Nov 2021 09:36:33 -0600
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 by: André G. Isaak - Wed, 3 Nov 2021 15:36 UTC

On 2021-11-03 08:48, olcott wrote:
> On 11/2/2021 10:30 PM, André G. Isaak wrote:
>> On 2021-11-02 21:14, olcott wrote:
>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>> On 2021-11-02 19:32, olcott wrote:
>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when
>>>>>>>>>>>>> it correctly reports what the actual behavior of its actual
>>>>>>>>>>>>> input would be then everyone (besides me) is wrong.
>>>>>>>>>>>>
>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it is
>>>>>>>>>>>> supposed to answer.
>>>>>>>>>>>>
>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>> *have* halting behaviour so your position above is entirely
>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>>>> running, or continue to run forever.
>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>
>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>
>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>> Linz's does not.
>>>>>>>>>>
>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>
>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>> identically to the actual TM being simulated. That means that
>>>>>>>>>> if the actual TM halts the simulation also must halt. Which
>>>>>>>>>> means that your simulation is not a 'correct simulation'.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>> simulation is correct.
>>>>>>>>
>>>>>>>> I have no idea what it means for a simulation of P(P) to "match
>>>>>>>> its x86 source code".
>>>>>>>>
>>>>>>>
>>>>>>> When the simulator executes the instructions at
>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>> of the x86 source code of P, then the simulator
>>>>>>> correctly simulated P(P).
>>>>>>
>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>> accurately duplicates *all* of the behaviour of that machine. Part
>>>>>> of the behaviour of P(P) is that it halts.
>>>>>>
>>>>>
>>>>> That is a stupid thing to say. The x86 emulator correctly emulates
>>>>> the x86 instructions of P iff it emulates the actual x86
>>>>> intructions of P saying anything else is both pure bullshit and
>>>>> quite nutty.
>>>>
>>>> That's a nonsensical claim. If it correctly emulates all the
>>>> instructions then it should have identical behaviour. That includes
>>>> whether it halts or not.
>>>
>>> Maybe you don't understand the x86 language well enough to ever
>>> understand what I am saying.
>>>
>>> While H continues to simulate P these first seven instructions of P
>>> continue to repeat. Do you understand that?
>>
>> Which is irrelevant to the halting problem
>
> I will not speak with you until you answer.

Whether it does or does not repeat cannot be determined from this trace
because you omit the instructions from the subroutine from your trace.

But this is a pointless diversion since it fails to address the more
fundamental point.

A halt decider takes a description of a Turing Machine w_M and an input
string and decides whether M will halt on input w. THAT IS THE
DEFINITION OF WHAT A HALT DECIDER DOES.

So given that P(P) halts, if H(P, P) returns 'false', then it is NOT
deciding correctly. Pouring over traces won't change this fact.

If I am tasked with writing a function which calculates sums and I come
up with the following:

int SUM(int x, int y) { return x * y; }

I can provide as many traces as I want. None of them are going to
somehow make SUM(5, 6) == 30 correct.

I can give you traces showing that this is the answer that my SUM *must*
arrive at. It doesn't make that the correct answer.

I can show you that SUM(0, 0) and SUM(2, 2) both give the mathematically
correct answer. This doesn't make the underlying logic correct.

If your function doesn't give an answer which corresponds to the correct
answer AS DEFINED BY THE SPECIFICATION, then it is wrong.

The specification for a halt decider demands that H(P, P) return TRUE
since P(P) halts. Nothing beyond this matters.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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 by: olcott - Wed, 3 Nov 2021 15:47 UTC

On 11/2/2021 10:17 PM, Ben Bacarisse wrote:
> olcott <polcott2@gmail.com> writes:
>
>> On 11/2/2021 12:25 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 11/2/2021 11:15 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>>>> As long as H(P,P)==0 is correct none of my other "errors" are of any
>>>>>> consequence what-so-ever.
>>>>>
>>>>> That's why I said one error really count: H(P,P)==0 is not correct
>>>>> because P(P) halts. How is it that you can keep ignoring this?
>>>>
>>>> It is a verified fact that for every possible (abort / do not abort)
>>>> behavior of every possible encoding of simulating halt decider H that
>>>> the input to H(P,P) never reaches its final state.
>>> H(P,P)==0 is wrong because P(P) halts. You keep trying to explain some
>>> other decision problem that you think H is getting right. For the
>>> halting problem -- the one you've been "studying" for more than 14 years
>>> -- H(P,P)==0 is only correct if P(P) does not halt and you've told us
>>> that is does.
>>>
>>>> It is like I am telling there are no integers between 1 and 2 and you
>>>> just don't believe it.
>>> No, its like you are tell me that H(P,P)==false is the right answer from
>>> a halt decider when P(P) is a halting computation. In fact it's very
>>> much like that. Almost exactly like that in fact.
>>>
>>>> It seems to be intuitively true that H(P,P) should report that its
>>>> input halts because P(P) halts.
>>> No. I have no intuition about what you even mean because inputs don't
>>> do anything. What is true by definition (no intuition required) is that
>>> H(P,P) should be false only if P(P) does not halt.
>>>
>>>> This intuition
>>> I don't have that intuition. What "the input" does is meaningless.
>>
>> Every halt decider is ONLY tasked with determining the behavior of its
>> input.
>
> No. Every halt decider is tasked with determining the behaviour of the
> computation represented by its input. That's why H(P,P)==0 is wrong.
> The arguments in that call represent the halting computation P(P).
>

THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
A halt decider only need answer whether or not the correct pure
simulation of its input would ever reach a final state of this input by
a simulating halt decider.

This addresses two issues, it focuses analysis on the correct point in
the execution trace.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It does not matter whether or not the halt decider at Ĥ.qx halts or not
the only thing that matters is whether or not the simulation of the
input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.

It acknowledges that inputs themselves only have behavior while they are
simulated.

>> That you say otherwise is very stupid.
>
> I say otherwise because I know what the halting problem is, and because
> I want to be careful about the details. You are deliberately not
> talking about what the input represents because you know H is wrong
> about that computation. This shift in wording is all you have left
> after 14 years of being wrong about halting.
>

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versus logic ]

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 by: olcott - Wed, 3 Nov 2021 15:50 UTC

On 11/2/2021 10:20 PM, Ben Bacarisse wrote:
> olcott <polcott2@gmail.com> writes:
>
>> On 11/2/2021 12:13 PM, Ben Bacarisse wrote:
>>> olcott <polcott2@gmail.com> writes:
>>>
>>>> On 11/2/2021 10:10 AM, Ben Bacarisse wrote:
>>>
>>>>> You want me to get sucked into discussing your other errors, but really
>>>>> only one counts: H(P,P) == false is the wrong answer if P(P) halts.
>>>>>
>>>> As long as H(P,P)==0 is correct none of my other "errors" are of any
>>>> consequence what-so-ever.
>>> Only one error really matters, and that's the fact that H(P,P)==0 is not
>>> correct if P(P) halts,
>>
>> As long as the input to H(P,P) cannot possibly halt for every possible
>> encoding of simulating halt decider H then H(P,P)==0 can't possibly be
>> incorrect NO MATTER WHAT.
>
> Whether H(P,P)==0 is correct is determined by what P(P) does, and since
> P(P) halts, H(P,P)==0 is wrong.
>

THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
A halt decider only need answer whether or not the correct pure
simulation of its input would ever reach a final state of this input by
a simulating halt decider.

This addresses two issues, it focuses analysis on the correct point in
the execution trace.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It does not matter whether or not the halt decider at Ĥ.qx halts or not
the only thing that matters is whether or not the simulation of the
input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.

It acknowledges that inputs themselves only have behavior while they are
simulated.

It does not matter what P(P) does it matters what the simulated input to
H(P,P) does.

H1(P,P) is computationally equivalent to P(P).
H(P,P) is not computationally equivalent to H1(P,P) or P(P).

>> If we have a black cat then it is utterly impossible that we do not
>> have a cat.
>
> We have a hating computation, P(P), and an H that is wrong about it. I
> don't know what all this nonsense about cats is intended to show.
>

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

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 by: olcott - Wed, 3 Nov 2021 15:53 UTC

On 11/3/2021 10:36 AM, André G. Isaak wrote:
> On 2021-11-03 08:48, olcott wrote:
>> On 11/2/2021 10:30 PM, André G. Isaak wrote:
>>> On 2021-11-02 21:14, olcott wrote:
>>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>>> On 2021-11-02 19:32, olcott wrote:
>>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when
>>>>>>>>>>>>>> it correctly reports what the actual behavior of its
>>>>>>>>>>>>>> actual input would be then everyone (besides me) is wrong.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it
>>>>>>>>>>>>> is supposed to answer.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>>> *have* halting behaviour so your position above is entirely
>>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>>>>> running, or continue to run forever.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>
>>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>>
>>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>>> Linz's does not.
>>>>>>>>>>>
>>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>>
>>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>>> identically to the actual TM being simulated. That means that
>>>>>>>>>>> if the actual TM halts the simulation also must halt. Which
>>>>>>>>>>> means that your simulation is not a 'correct simulation'.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>>> simulation is correct.
>>>>>>>>>
>>>>>>>>> I have no idea what it means for a simulation of P(P) to "match
>>>>>>>>> its x86 source code".
>>>>>>>>>
>>>>>>>>
>>>>>>>> When the simulator executes the instructions at
>>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>>> of the x86 source code of P, then the simulator
>>>>>>>> correctly simulated P(P).
>>>>>>>
>>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>>> accurately duplicates *all* of the behaviour of that machine.
>>>>>>> Part of the behaviour of P(P) is that it halts.
>>>>>>>
>>>>>>
>>>>>> That is a stupid thing to say. The x86 emulator correctly emulates
>>>>>> the x86 instructions of P iff it emulates the actual x86
>>>>>> intructions of P saying anything else is both pure bullshit and
>>>>>> quite nutty.
>>>>>
>>>>> That's a nonsensical claim. If it correctly emulates all the
>>>>> instructions then it should have identical behaviour. That includes
>>>>> whether it halts or not.
>>>>
>>>> Maybe you don't understand the x86 language well enough to ever
>>>> understand what I am saying.
>>>>
>>>> While H continues to simulate P these first seven instructions of P
>>>> continue to repeat. Do you understand that?
>>>
>>> Which is irrelevant to the halting problem
>>
>> I will not speak with you until you answer.
>
> Whether it does or does not repeat cannot be determined from this trace
> because you omit the instructions from the subroutine from your trace.
>

Begin Local Halt Decider Simulation at Machine Address:c36

machine stack stack machine assembly
address address data code language
======== ======== ======== ========= =============
[00000c36][002117ca][002117ce] 55 push ebp
[00000c37][002117ca][002117ce] 8bec mov ebp,esp
[00000c39][002117ca][002117ce] 8b4508 mov eax,[ebp+08]
[00000c3c][002117c6][00000c36] 50 push eax // push P
[00000c3d][002117c6][00000c36] 8b4d08 mov ecx,[ebp+08]
[00000c40][002117c2][00000c36] 51 push ecx // push P
[00000c41][002117be][00000c46] e820fdffff call 00000966 // call H(P,P)

When it is given that H is a pure simulator of its input can you
comprhend that the above seven lines infinitely repeat?

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 10:00:45 -0600
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 by: André G. Isaak - Wed, 3 Nov 2021 16:00 UTC

On 2021-11-03 09:47, olcott wrote:

> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
> A halt decider only need answer whether or not the correct pure
> simulation of its input would ever reach a final state of this input by
> a simulating halt decider.

The halting problem already defines what the criterion used by a halt
decider must be. You don't get to update it if that's the problem you
want to work on.

André

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Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
impossibly incorrect ]
Date: Wed, 3 Nov 2021 10:06:41 -0600
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 by: André G. Isaak - Wed, 3 Nov 2021 16:06 UTC

On 2021-11-03 09:53, olcott wrote:
> On 11/3/2021 10:36 AM, André G. Isaak wrote:
>> On 2021-11-03 08:48, olcott wrote:
>>> On 11/2/2021 10:30 PM, André G. Isaak wrote:
>>>> On 2021-11-02 21:14, olcott wrote:
>>>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>>>> On 2021-11-02 19:32, olcott wrote:
>>>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong when
>>>>>>>>>>>>>>> it correctly reports what the actual behavior of its
>>>>>>>>>>>>>>> actual input would be then everyone (besides me) is wrong.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it
>>>>>>>>>>>>>> is supposed to answer.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>>>> *have* halting behaviour so your position above is
>>>>>>>>>>>>>> entirely incoherent.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>>>>>> running, or continue to run forever.
>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>>
>>>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>>>
>>>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>>>> Linz's does not.
>>>>>>>>>>>>
>>>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>>>
>>>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>>>> identically to the actual TM being simulated. That means
>>>>>>>>>>>> that if the actual TM halts the simulation also must halt.
>>>>>>>>>>>> Which means that your simulation is not a 'correct simulation'.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>>>> simulation is correct.
>>>>>>>>>>
>>>>>>>>>> I have no idea what it means for a simulation of P(P) to
>>>>>>>>>> "match its x86 source code".
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When the simulator executes the instructions at
>>>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>>>> of the x86 source code of P, then the simulator
>>>>>>>>> correctly simulated P(P).
>>>>>>>>
>>>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>>>> accurately duplicates *all* of the behaviour of that machine.
>>>>>>>> Part of the behaviour of P(P) is that it halts.
>>>>>>>>
>>>>>>>
>>>>>>> That is a stupid thing to say. The x86 emulator correctly
>>>>>>> emulates the x86 instructions of P iff it emulates the actual x86
>>>>>>> intructions of P saying anything else is both pure bullshit and
>>>>>>> quite nutty.
>>>>>>
>>>>>> That's a nonsensical claim. If it correctly emulates all the
>>>>>> instructions then it should have identical behaviour. That
>>>>>> includes whether it halts or not.
>>>>>
>>>>> Maybe you don't understand the x86 language well enough to ever
>>>>> understand what I am saying.
>>>>>
>>>>> While H continues to simulate P these first seven instructions of P
>>>>> continue to repeat. Do you understand that?
>>>>
>>>> Which is irrelevant to the halting problem
>>>
>>> I will not speak with you until you answer.
>>
>> Whether it does or does not repeat cannot be determined from this
>> trace because you omit the instructions from the subroutine from your
>> trace.
>>
>
> Begin Local Halt Decider Simulation at Machine Address:c36
>
>  machine   stack     stack     machine    assembly
>  address   address   data      code       language
>  ========  ========  ========  =========  =============
> [00000c36][002117ca][002117ce] 55          push ebp
> [00000c37][002117ca][002117ce] 8bec        mov ebp,esp
> [00000c39][002117ca][002117ce] 8b4508      mov eax,[ebp+08]
> [00000c3c][002117c6][00000c36] 50          push eax       // push P
> [00000c3d][002117c6][00000c36] 8b4d08      mov ecx,[ebp+08]
> [00000c40][002117c2][00000c36] 51          push ecx       // push P
> [00000c41][002117be][00000c46] e820fdffff  call 00000966  // call H(P,P)
>
> When it is given that H is a pure simulator of its input can you
> comprhend that the above seven lines infinitely repeat?

Nothing in the above seven lines indicates that they would repeat since
there is no instruction there which branches back to c36.

But, again, all of this is besides the point. A halt decider is supposed
to determine whether the machine described by its input halts on a given
input. You acknowledge that P(P) halts. Therefore H(P, P) == 0 is
incorrect. We don't need to look at a trace to know that the answer is
wrong. We just need to compare the result which H(P, P) returns with the
correct answer.

André

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Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
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 by: olcott - Wed, 3 Nov 2021 16:14 UTC

On 11/3/2021 11:00 AM, André G. Isaak wrote:
> On 2021-11-03 09:47, olcott wrote:
>
>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>> A halt decider only need answer whether or not the correct pure
>> simulation of its input would ever reach a final state of this input
>> by a simulating halt decider.
>
> The halting problem already defines what the criterion used by a halt
> decider must be. You don't get to update it if that's the problem you
> want to work on.
>
> André
>

No one here seems capable of understanding is that when a halt decider
does correctly decide the halt status of its input then its input has
had its halt status correctly decided.

Even Linz got confused about this.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It does not matter whether or not the halt decider at Ĥ.qx halts or not
the only thing that matters is whether or not the simulation of the
input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.

The mistake is just like putting Bill Smith in jail for robbing a liquor
store because Bill Jones did Rob a liquor store.

As long as a halt decider does correctly decide the halt status of its
input nothing else in the universe can show that the halt decider is
incorrect.

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]
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 by: Ben Bacarisse - Wed, 3 Nov 2021 16:15 UTC

olcott <NoOne@NoWhere.com> writes:

> On 11/2/2021 10:17 PM, Ben Bacarisse wrote:
>> olcott <polcott2@gmail.com> writes:

>>> Every halt decider is ONLY tasked with determining the behavior of its
>>> input.
>>
>> No. Every halt decider is tasked with determining the behaviour of the
>> computation represented by its input. That's why H(P,P)==0 is wrong.
>> The arguments in that call represent the halting computation P(P).
>
> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
> A halt decider only need answer whether or not the correct pure
> simulation of its input would ever reach a final state of this input
> by a simulating halt decider.

The halting problem is already defined, thank you. H(P,P) == false is
wrong because P(P) halts.

--
Ben.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versus logic ]

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versus logic ]
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 by: Ben Bacarisse - Wed, 3 Nov 2021 16:18 UTC

olcott <NoOne@NoWhere.com> writes:

> On 11/2/2021 10:20 PM, Ben Bacarisse wrote:
>> olcott <polcott2@gmail.com> writes:
>>
>>> On 11/2/2021 12:13 PM, Ben Bacarisse wrote:
>>>> olcott <polcott2@gmail.com> writes:
>>>>
>>>>> On 11/2/2021 10:10 AM, Ben Bacarisse wrote:
>>>>
>>>>>> You want me to get sucked into discussing your other errors, but really
>>>>>> only one counts: H(P,P) == false is the wrong answer if P(P) halts.
>>>>>>
>>>>> As long as H(P,P)==0 is correct none of my other "errors" are of any
>>>>> consequence what-so-ever.
>>>> Only one error really matters, and that's the fact that H(P,P)==0 is not
>>>> correct if P(P) halts,
>>>
>>> As long as the input to H(P,P) cannot possibly halt for every possible
>>> encoding of simulating halt decider H then H(P,P)==0 can't possibly be
>>> incorrect NO MATTER WHAT.
>> Whether H(P,P)==0 is correct is determined by what P(P) does, and since
>> P(P) halts, H(P,P)==0 is wrong.
>
> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
> A halt decider only need answer whether or not the correct pure
> simulation of its input would ever reach a final state of this input
> by a simulating halt decider.

We could problem just have one sub-thread about this. What I said both
above and in my other reply still applied no matter how many times you
re-write your criterion.

--
Ben.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ impossibly incorrect ]

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 by: olcott - Wed, 3 Nov 2021 16:20 UTC

On 11/3/2021 11:06 AM, André G. Isaak wrote:
> On 2021-11-03 09:53, olcott wrote:
>> On 11/3/2021 10:36 AM, André G. Isaak wrote:
>>> On 2021-11-03 08:48, olcott wrote:
>>>> On 11/2/2021 10:30 PM, André G. Isaak wrote:
>>>>> On 2021-11-02 21:14, olcott wrote:
>>>>>> On 11/2/2021 9:26 PM, André G. Isaak wrote:
>>>>>>> On 2021-11-02 19:32, olcott wrote:
>>>>>>>> On 11/2/2021 8:07 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-11-02 18:49, olcott wrote:
>>>>>>>>>> On 11/2/2021 6:31 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-11-02 16:51, olcott wrote:
>>>>>>>>>>>> On 11/2/2021 4:49 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2021-11-02 15:41, olcott wrote:
>>>>>>>>>>>>>> On 11/2/2021 4:05 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>> On 2021-11-02 14:43, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If everyone "defines" that the halt decider is wrong
>>>>>>>>>>>>>>>> when it correctly reports what the actual behavior of
>>>>>>>>>>>>>>>> its actual input would be then everyone (besides me) is
>>>>>>>>>>>>>>>> wrong.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The definition tells you what a halt decider *is*. It
>>>>>>>>>>>>>>> doesn't define it as 'wrong'. It defines what question it
>>>>>>>>>>>>>>> is supposed to answer.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The input to a halt decider is a string. Strings don't
>>>>>>>>>>>>>>> *have* halting behaviour so your position above is
>>>>>>>>>>>>>>> entirely incoherent.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In computability theory, the halting problem is the
>>>>>>>>>>>>>> problem of determining, from a description of an arbitrary
>>>>>>>>>>>>>> computer program and an input, whether the program will
>>>>>>>>>>>>>> finish running, or continue to run forever.
>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>>>
>>>>>>>>>>>>> The definition of 'halting problem' is what it is.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Note that the above definition doesn't make any mentions of
>>>>>>>>>>>>> 'simulations' just as the more formal definition used by
>>>>>>>>>>>>> Linz's does not.
>>>>>>>>>>>>>
>>>>>>>>>>>>>> A halt decider only need answer whether or not the correct
>>>>>>>>>>>>>> simulation of its input would ever reach a final state of
>>>>>>>>>>>>>> this input by a simulating halt decider.
>>>>>>>>>>>>>
>>>>>>>>>>>>> A 'correct simulation', presumably, would be one that acts
>>>>>>>>>>>>> identically to the actual TM being simulated. That means
>>>>>>>>>>>>> that if the actual TM halts the simulation also must halt.
>>>>>>>>>>>>> Which means that your simulation is not a 'correct
>>>>>>>>>>>>> simulation'.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> There are no freaking presumptions about it. As long as the
>>>>>>>>>>>> simulation of P(P) matches its x86 source code then the
>>>>>>>>>>>> simulation is correct.
>>>>>>>>>>>
>>>>>>>>>>> I have no idea what it means for a simulation of P(P) to
>>>>>>>>>>> "match its x86 source code".
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When the simulator executes the instructions at
>>>>>>>>>> 0xc36, 0xc37, 0xc39, 0xc3c, 0xc3d, 0xc40, 0xc41
>>>>>>>>>> of the x86 source code of P, then the simulator
>>>>>>>>>> correctly simulated P(P).
>>>>>>>>>
>>>>>>>>> No. A simulator only 'correctly simulates' a machine when it
>>>>>>>>> accurately duplicates *all* of the behaviour of that machine.
>>>>>>>>> Part of the behaviour of P(P) is that it halts.
>>>>>>>>>
>>>>>>>>
>>>>>>>> That is a stupid thing to say. The x86 emulator correctly
>>>>>>>> emulates the x86 instructions of P iff it emulates the actual
>>>>>>>> x86 intructions of P saying anything else is both pure bullshit
>>>>>>>> and quite nutty.
>>>>>>>
>>>>>>> That's a nonsensical claim. If it correctly emulates all the
>>>>>>> instructions then it should have identical behaviour. That
>>>>>>> includes whether it halts or not.
>>>>>>
>>>>>> Maybe you don't understand the x86 language well enough to ever
>>>>>> understand what I am saying.
>>>>>>
>>>>>> While H continues to simulate P these first seven instructions of
>>>>>> P continue to repeat. Do you understand that?
>>>>>
>>>>> Which is irrelevant to the halting problem
>>>>
>>>> I will not speak with you until you answer.
>>>
>>> Whether it does or does not repeat cannot be determined from this
>>> trace because you omit the instructions from the subroutine from your
>>> trace.
>>>
>>
>> Begin Local Halt Decider Simulation at Machine Address:c36
>>
>>   machine   stack     stack     machine    assembly
>>   address   address   data      code       language
>>   ========  ========  ========  =========  =============
>> [00000c36][002117ca][002117ce] 55          push ebp
>> [00000c37][002117ca][002117ce] 8bec        mov ebp,esp
>> [00000c39][002117ca][002117ce] 8b4508      mov eax,[ebp+08]
>> [00000c3c][002117c6][00000c36] 50          push eax       // push P
>> [00000c3d][002117c6][00000c36] 8b4d08      mov ecx,[ebp+08]
>> [00000c40][002117c2][00000c36] 51          push ecx       // push P
>> [00000c41][002117be][00000c46] e820fdffff  call 00000966  // call H(P,P)
>>
>> When it is given that H is a pure simulator of its input can you
>> comprhend that the above seven lines infinitely repeat?
>
> Nothing in the above seven lines indicates that they would repeat since
> there is no instruction there which branches back to c36.
>

If you look in the stack data column in the // push P rows
you will see that H is being called with 0xc36

Because I already told you to assume the line c41 of P calls
H as a pure simulator. It already says on lines c3c and c40
that P is being pushed onto the stack.

When P calls H with itself as input on c41 and H is only a pure
simulator of its input can you see that these first seven lines would
infinitely repeat?

_P()
[00000c36](01) 55 push ebp
[00000c37](02) 8bec mov ebp,esp
[00000c39](03) 8b4508 mov eax,[ebp+08] // 2nd Param
[00000c3c](01) 50 push eax
[00000c3d](03) 8b4d08 mov ecx,[ebp+08] // 1st Param
[00000c40](01) 51 push ecx
[00000c41](05) e820fdffff call 00000966 // call H
[00000c46](03) 83c408 add esp,+08
[00000c49](02) 85c0 test eax,eax
[00000c4b](02) 7402 jz 00000c4f
[00000c4d](02) ebfe jmp 00000c4d
[00000c4f](01) 5d pop ebp
[00000c50](01) c3 ret
Size in bytes:(0027) [00000c50]


Click here to read the complete article
Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]
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 by: Ben Bacarisse - Wed, 3 Nov 2021 16:25 UTC

olcott <NoOne@NoWhere.com> writes:

> No one here seems capable of understanding is that when a halt decider
> does correctly decide the halt status of its input then its input has
> had its halt status correctly decided.

Don't be silly. No one disputes that (thought the wording is poor).
The only disagreement is on what the correct answer is. Since P(P)
halts and H(P,P) == false, H is not deciding correctly.

--
Ben.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
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 by: olcott - Wed, 3 Nov 2021 16:25 UTC

On 11/3/2021 11:15 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 11/2/2021 10:17 PM, Ben Bacarisse wrote:
>>> olcott <polcott2@gmail.com> writes:
>
>>>> Every halt decider is ONLY tasked with determining the behavior of its
>>>> input.
>>>
>>> No. Every halt decider is tasked with determining the behaviour of the
>>> computation represented by its input. That's why H(P,P)==0 is wrong.
>>> The arguments in that call represent the halting computation P(P).
>>
>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>> A halt decider only need answer whether or not the correct pure
>> simulation of its input would ever reach a final state of this input
>> by a simulating halt decider.
>
> The halting problem is already defined, thank you. H(P,P) == false is
> wrong because P(P) halts.
>

So in other words when H correctly determines that its input never
reaches its final state the fact that some other entirely different
computation does reach its final state proves that H is wrong?

H1(P,P) is computationally equivalent to P(P)
H(P,P) is NOT computationally equivalent to either P(P) or H1(P,P).

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ intuition versus logic ]

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 by: olcott - Wed, 3 Nov 2021 16:26 UTC

On 11/3/2021 11:18 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 11/2/2021 10:20 PM, Ben Bacarisse wrote:
>>> olcott <polcott2@gmail.com> writes:
>>>
>>>> On 11/2/2021 12:13 PM, Ben Bacarisse wrote:
>>>>> olcott <polcott2@gmail.com> writes:
>>>>>
>>>>>> On 11/2/2021 10:10 AM, Ben Bacarisse wrote:
>>>>>
>>>>>>> You want me to get sucked into discussing your other errors, but really
>>>>>>> only one counts: H(P,P) == false is the wrong answer if P(P) halts.
>>>>>>>
>>>>>> As long as H(P,P)==0 is correct none of my other "errors" are of any
>>>>>> consequence what-so-ever.
>>>>> Only one error really matters, and that's the fact that H(P,P)==0 is not
>>>>> correct if P(P) halts,
>>>>
>>>> As long as the input to H(P,P) cannot possibly halt for every possible
>>>> encoding of simulating halt decider H then H(P,P)==0 can't possibly be
>>>> incorrect NO MATTER WHAT.
>>> Whether H(P,P)==0 is correct is determined by what P(P) does, and since
>>> P(P) halts, H(P,P)==0 is wrong.
>>
>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>> A halt decider only need answer whether or not the correct pure
>> simulation of its input would ever reach a final state of this input
>> by a simulating halt decider.
>
> We could problem just have one sub-thread about this. What I said both
> above and in my other reply still applied no matter how many times you
> re-write your criterion.
>

So in other words when H correctly determines that its input never
reaches its final state the fact that some other entirely different
computation does reach its final state proves that H is wrong?

H1(P,P) is computationally equivalent to P(P)
H(P,P) is NOT computationally equivalent to either P(P) or H1(P,P).

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ][ Linz mistake ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ][ Linz mistake ]
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 by: olcott - Wed, 3 Nov 2021 16:33 UTC

On 11/3/2021 11:25 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> No one here seems capable of understanding is that when a halt decider
>> does correctly decide the halt status of its input then its input has
>> had its halt status correctly decided.
>
> Don't be silly. No one disputes that (thought the wording is poor).
> The only disagreement is on what the correct answer is. Since P(P)
> halts and H(P,P) == false, H is not deciding correctly.
>

THE MOST RECENT UPDATE TO THE CRITERION MEASURE
A halt decider only need answer whether or not the correct pure
simulation of its input would ever reach a final state of this input by
a simulating halt decider.

Even Linz got confused about this:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

It does not matter whether or not the halt decider at Ĥ.qx halts or not
the only thing that matters is whether or not the simulation of the
input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.

Top of page 320
https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf

Linz believes that when Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn because its input never
halts this is nonsense because Ĥ does halt.

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

<slufo0$t8l$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=22963&group=comp.theory#22963

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 11:09:18 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Wed, 3 Nov 2021 17:09 UTC

On 2021-11-03 10:14, olcott wrote:
> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>> On 2021-11-03 09:47, olcott wrote:
>>
>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>> A halt decider only need answer whether or not the correct pure
>>> simulation of its input would ever reach a final state of this input
>>> by a simulating halt decider.
>>
>> The halting problem already defines what the criterion used by a halt
>> decider must be. You don't get to update it if that's the problem you
>> want to work on.
>>
>> André
>>
>
> No one here seems capable of understanding is that when a halt decider
> does correctly decide the halt status of its input then its input has
> had its halt status correctly decided.

Right. And since yours doesn't correctly decide the halt status of its
input then its input has not had its halt status correctly decided.

The correct decision is the one which correctly answers the question
specified by the actual halting problem: Does the Turing Machine
represented by the input string halt on the given input?

> Even Linz got confused about this.
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> It does not matter whether or not the halt decider at Ĥ.qx halts or not
> the only thing that matters is whether or not the simulation of the
> input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.

Linz isn't confused at all. You just don't understand the above
notation. Ĥ.qx is a *state*, not a halt decider. States don't halt.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

<slufu5$us7$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 11:12:35 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Wed, 3 Nov 2021 17:12 UTC

On 2021-11-03 10:25, olcott wrote:
> On 11/3/2021 11:15 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 11/2/2021 10:17 PM, Ben Bacarisse wrote:
>>>> olcott <polcott2@gmail.com> writes:
>>
>>>>> Every halt decider is ONLY tasked with determining the behavior of its
>>>>> input.
>>>>
>>>> No.  Every halt decider is tasked with determining the behaviour of the
>>>> computation represented by its input.  That's why H(P,P)==0 is wrong.
>>>> The arguments in that call represent the halting computation P(P).
>>>
>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>> A halt decider only need answer whether or not the correct pure
>>> simulation of its input would ever reach a final state of this input
>>> by a simulating halt decider.
>>
>> The halting problem is already defined, thank you.  H(P,P) == false is
>> wrong because P(P) halts.
>>
>
> So in other words when H correctly determines that its input never
> reaches its final state the fact that some other entirely different
> computation does reach its final state proves that H is wrong?

P(P) is *not* some entirely different computation. it's the computation
which H(P, P) is being asked to decide about. READ THE DEFINITION OF
HALT DECIDER.

The input is just a string. Strings don't have final states. What
matters is the actual computation represented by that string, which is P(P)

> H1(P,P) is computationally equivalent to P(P)
> H(P,P) is NOT computationally equivalent to either P(P) or H1(P,P).
Neither of these are computationally equivalent to P(P). Why you keep
saying this is beyond me. But in both cases, the *input* is a
representation of P(P) which means that P(P) is the computation whose
halting status must be decided.

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
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 by: olcott - Wed, 3 Nov 2021 17:19 UTC

On 11/3/2021 12:09 PM, André G. Isaak wrote:
> On 2021-11-03 10:14, olcott wrote:
>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>> On 2021-11-03 09:47, olcott wrote:
>>>
>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>> A halt decider only need answer whether or not the correct pure
>>>> simulation of its input would ever reach a final state of this input
>>>> by a simulating halt decider.
>>>
>>> The halting problem already defines what the criterion used by a halt
>>> decider must be. You don't get to update it if that's the problem you
>>> want to work on.
>>>
>>> André
>>>
>>
>> No one here seems capable of understanding is that when a halt decider
>> does correctly decide the halt status of its input then its input has
>> had its halt status correctly decided.
>
> Right. And since yours doesn't correctly decide the halt status of its
> input then its input has not had its halt status correctly decided.
>

The only criteria for correctly deciding the halt status of the actual
input is whether or not the correct pure simulation of this input would
ever reach a final state.

Every other criteria changes the subject to an entirely different
comutation.

> The correct decision is the one which correctly answers the question
> specified by the actual halting problem: Does the Turing Machine
> represented by the input string halt on the given input?
>
>> Even Linz got confused about this.
>>
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>> It does not matter whether or not the halt decider at Ĥ.qx halts or
>> not the only thing that matters is whether or not the simulation of
>> the input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ever reaches a final state.
>
> Linz isn't confused at all. You just don't understand the above
> notation. Ĥ.qx is a *state*, not a halt decider. States don't halt.
>
> André
>

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

<sluhq6$dsk$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 11:44:37 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Wed, 3 Nov 2021 17:44 UTC

On 2021-11-03 11:19, olcott wrote:
> On 11/3/2021 12:09 PM, André G. Isaak wrote:
>> On 2021-11-03 10:14, olcott wrote:
>>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>>> On 2021-11-03 09:47, olcott wrote:
>>>>
>>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>>> A halt decider only need answer whether or not the correct pure
>>>>> simulation of its input would ever reach a final state of this
>>>>> input by a simulating halt decider.
>>>>
>>>> The halting problem already defines what the criterion used by a
>>>> halt decider must be. You don't get to update it if that's the
>>>> problem you want to work on.
>>>>
>>>> André
>>>>
>>>
>>> No one here seems capable of understanding is that when a halt
>>> decider does correctly decide the halt status of its input then its
>>> input has had its halt status correctly decided.
>>
>> Right. And since yours doesn't correctly decide the halt status of its
>> input then its input has not had its halt status correctly decided.
>>
>
> The only criteria for correctly deciding the halt status of the actual
> input is whether or not the correct pure simulation of this input would
> ever reach a final state.
>
> Every other criteria changes the subject to an entirely different
> comutation.

Both 'halting problem' and 'halt decider' were defined before you were
born by people who actually UNDERSTOOD the topic.

The definitions of these things are precise, unambiguous, and clearly
indicate the actual criterion which a halt decider must use in making
its decision. That criterion makes no reference to pure simulations. It
refers only to whether the computation represented by the input string
halts.

The only one changing the subject to an entirely different computation
is you. If you want to discuss the halting problem or halt deciders, you
must use the actual definitions of these things. And the actual
definitions make it clear that if H(P, P) is actually a halt decider it
must correctly describe the actual behaviour of P(P).

A halt decider is correct in deciding that the input (P, P) doesn't halt
if and only if P(P) doesn't halt.

Absolutely no one here is going to retreat from the above statement
because that is how the halting problem is defined. Looking at traces
cannot change fundamental definitions. Looking at traces cannot change
the fact that P(P) as written halts. 'Revising' the halting criterion
can have no effect on the actual halting criterion which is the only one
that anyone working on compututional theory cares about.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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updated criterion ]
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 by: olcott - Wed, 3 Nov 2021 18:23 UTC

On 11/3/2021 12:44 PM, André G. Isaak wrote:
> On 2021-11-03 11:19, olcott wrote:
>> On 11/3/2021 12:09 PM, André G. Isaak wrote:
>>> On 2021-11-03 10:14, olcott wrote:
>>>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>>>> On 2021-11-03 09:47, olcott wrote:
>>>>>
>>>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>>>> A halt decider only need answer whether or not the correct pure
>>>>>> simulation of its input would ever reach a final state of this
>>>>>> input by a simulating halt decider.
>>>>>
>>>>> The halting problem already defines what the criterion used by a
>>>>> halt decider must be. You don't get to update it if that's the
>>>>> problem you want to work on.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> No one here seems capable of understanding is that when a halt
>>>> decider does correctly decide the halt status of its input then its
>>>> input has had its halt status correctly decided.
>>>
>>> Right. And since yours doesn't correctly decide the halt status of
>>> its input then its input has not had its halt status correctly decided.
>>>
>>
>> The only criteria for correctly deciding the halt status of the actual
>> input is whether or not the correct pure simulation of this input
>> would ever reach a final state.
>>
>> Every other criteria changes the subject to an entirely different
>> comutation.
>
>
> Both 'halting problem' and 'halt decider' were defined before you were
> born by people who actually UNDERSTOOD the topic.
>
> The definitions of these things are precise, unambiguous, and clearly
> indicate the actual criterion which a halt decider must use in making
> its decision. That criterion makes no reference to pure simulations. It
> refers only to whether the computation represented by the input string
> halts.
>

It is impossible for any halt decider to be incorrect when the correct
pure simulation of its input never halts and it reports not halting.

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

<slumbk$iqu$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 13:02:11 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Wed, 3 Nov 2021 19:02 UTC

On 2021-11-03 12:23, olcott wrote:
> On 11/3/2021 12:44 PM, André G. Isaak wrote:
>> On 2021-11-03 11:19, olcott wrote:
>>> On 11/3/2021 12:09 PM, André G. Isaak wrote:
>>>> On 2021-11-03 10:14, olcott wrote:
>>>>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>>>>> On 2021-11-03 09:47, olcott wrote:
>>>>>>
>>>>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>>>>> A halt decider only need answer whether or not the correct pure
>>>>>>> simulation of its input would ever reach a final state of this
>>>>>>> input by a simulating halt decider.
>>>>>>
>>>>>> The halting problem already defines what the criterion used by a
>>>>>> halt decider must be. You don't get to update it if that's the
>>>>>> problem you want to work on.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> No one here seems capable of understanding is that when a halt
>>>>> decider does correctly decide the halt status of its input then its
>>>>> input has had its halt status correctly decided.
>>>>
>>>> Right. And since yours doesn't correctly decide the halt status of
>>>> its input then its input has not had its halt status correctly decided.
>>>>
>>>
>>> The only criteria for correctly deciding the halt status of the
>>> actual input is whether or not the correct pure simulation of this
>>> input would ever reach a final state.
>>>
>>> Every other criteria changes the subject to an entirely different
>>> comutation.
>>
>>
>> Both 'halting problem' and 'halt decider' were defined before you were
>> born by people who actually UNDERSTOOD the topic.
>>
>> The definitions of these things are precise, unambiguous, and clearly
>> indicate the actual criterion which a halt decider must use in making
>> its decision. That criterion makes no reference to pure simulations.
>> It refers only to whether the computation represented by the input
>> string halts.
>>
>
> It is impossible for any halt decider to be incorrect when the correct
> pure simulation of its input never halts and it reports not halting.

Not if it contradicts the actual correct answer as determined by the
criterion which defines the halting problem since that criterion alone
determines which answer is correct.

And your H does not give the correct answer for P(P) even if "the
correct pure simulation of its input never halts and it reports not
halting."

There are several possible explanations for this:

(a) Your "revised" criterion is not equivalent to the one which defines
the problem and thus your H is not addressing the actual halting problem.

(b) Your H is buggy and therefore is not returning the answer it should.

(c) The internal logic of your H doesn't actually implement the
criterion you claim it does.

(d) Your criterion is so poorly stated and involves so much equivocation
that it isn't even possible to determine whether something meets it or not.

(e) More than one of the above

(f) All of the above.

My money's on (f).

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

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Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
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 by: olcott - Wed, 3 Nov 2021 20:02 UTC

On 11/3/2021 2:02 PM, André G. Isaak wrote:
> On 2021-11-03 12:23, olcott wrote:
>> On 11/3/2021 12:44 PM, André G. Isaak wrote:
>>> On 2021-11-03 11:19, olcott wrote:
>>>> On 11/3/2021 12:09 PM, André G. Isaak wrote:
>>>>> On 2021-11-03 10:14, olcott wrote:
>>>>>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>>>>>> On 2021-11-03 09:47, olcott wrote:
>>>>>>>
>>>>>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>>>>>> A halt decider only need answer whether or not the correct pure
>>>>>>>> simulation of its input would ever reach a final state of this
>>>>>>>> input by a simulating halt decider.
>>>>>>>
>>>>>>> The halting problem already defines what the criterion used by a
>>>>>>> halt decider must be. You don't get to update it if that's the
>>>>>>> problem you want to work on.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> No one here seems capable of understanding is that when a halt
>>>>>> decider does correctly decide the halt status of its input then
>>>>>> its input has had its halt status correctly decided.
>>>>>
>>>>> Right. And since yours doesn't correctly decide the halt status of
>>>>> its input then its input has not had its halt status correctly
>>>>> decided.
>>>>>
>>>>
>>>> The only criteria for correctly deciding the halt status of the
>>>> actual input is whether or not the correct pure simulation of this
>>>> input would ever reach a final state.
>>>>
>>>> Every other criteria changes the subject to an entirely different
>>>> comutation.
>>>
>>>
>>> Both 'halting problem' and 'halt decider' were defined before you
>>> were born by people who actually UNDERSTOOD the topic.
>>>
>>> The definitions of these things are precise, unambiguous, and clearly
>>> indicate the actual criterion which a halt decider must use in making
>>> its decision. That criterion makes no reference to pure simulations.
>>> It refers only to whether the computation represented by the input
>>> string halts.
>>>
>>
>> It is impossible for any halt decider to be incorrect when the correct
>> pure simulation of its input never halts and it reports not halting.
>
> Not if it contradicts the actual correct answer as determined by the
> criterion which defines the halting problem since that criterion alone
> determines which answer is correct.
It is impossible for any halt decider to be incorrect when the correct
pure simulation of its input never halts and it reports not halting.

In the same way and to the same degree that it is impossible for an
animal that is a cat and not a dog to be a dog and not a cat.

You just aren't paying enough attention to the meaning of the words.

--
Copyright 2021 Pete Olcott

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

Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [ updated criterion ]

<slutej$a29$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: H(P,P)==0 is correct for every simulating halt decider H --- V2 [
updated criterion ]
Date: Wed, 3 Nov 2021 15:03:14 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Wed, 3 Nov 2021 21:03 UTC

On 2021-11-03 14:02, olcott wrote:
> On 11/3/2021 2:02 PM, André G. Isaak wrote:
>> On 2021-11-03 12:23, olcott wrote:
>>> On 11/3/2021 12:44 PM, André G. Isaak wrote:
>>>> On 2021-11-03 11:19, olcott wrote:
>>>>> On 11/3/2021 12:09 PM, André G. Isaak wrote:
>>>>>> On 2021-11-03 10:14, olcott wrote:
>>>>>>> On 11/3/2021 11:00 AM, André G. Isaak wrote:
>>>>>>>> On 2021-11-03 09:47, olcott wrote:
>>>>>>>>
>>>>>>>>> THE IS THE MOST RECENT UPDATE TO THE CRITERION MEASURE
>>>>>>>>> A halt decider only need answer whether or not the correct pure
>>>>>>>>> simulation of its input would ever reach a final state of this
>>>>>>>>> input by a simulating halt decider.
>>>>>>>>
>>>>>>>> The halting problem already defines what the criterion used by a
>>>>>>>> halt decider must be. You don't get to update it if that's the
>>>>>>>> problem you want to work on.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> No one here seems capable of understanding is that when a halt
>>>>>>> decider does correctly decide the halt status of its input then
>>>>>>> its input has had its halt status correctly decided.
>>>>>>
>>>>>> Right. And since yours doesn't correctly decide the halt status of
>>>>>> its input then its input has not had its halt status correctly
>>>>>> decided.
>>>>>>
>>>>>
>>>>> The only criteria for correctly deciding the halt status of the
>>>>> actual input is whether or not the correct pure simulation of this
>>>>> input would ever reach a final state.
>>>>>
>>>>> Every other criteria changes the subject to an entirely different
>>>>> comutation.
>>>>
>>>>
>>>> Both 'halting problem' and 'halt decider' were defined before you
>>>> were born by people who actually UNDERSTOOD the topic.
>>>>
>>>> The definitions of these things are precise, unambiguous, and
>>>> clearly indicate the actual criterion which a halt decider must use
>>>> in making its decision. That criterion makes no reference to pure
>>>> simulations. It refers only to whether the computation represented
>>>> by the input string halts.
>>>>
>>>
>>> It is impossible for any halt decider to be incorrect when the
>>> correct pure simulation of its input never halts and it reports not
>>> halting.
>>
>> Not if it contradicts the actual correct answer as determined by the
>> criterion which defines the halting problem since that criterion alone
>> determines which answer is correct.
> It is impossible for any halt decider to be incorrect when the correct
> pure simulation of its input never halts and it reports not halting.

But your halt decider doesn't implement a 'pure simulation' under any
reasonable definition of the term. A pure simulation which does not halt
runs forever, so if your decider actually implemented a pure simulation
it could not possibly report 'not halting'.

You seem to either not grasp the concept of a 'definition' or don't
understand what the word 'correct' means.

The definition of a halt decider defines *precisely* the criterion which
determines which answer is correct for a given input. That's the *only*
criterion which matters.

For H(P, P), the correct answer is true if and only if P(P) halts. And,
since P(P) does halt, the correct answer is true.

The definition provides the SOLE, DEFINITIVE criterion for determining
which answer is correct. No other criterion can possibly be correct if
it does not match the one in the definition in all possible cases. Why
you insist on continuing to argue that H(P, P) == 0 is correct given
that you acknowledge that P(P) halts is entirely beyond me.

> In the same way and to the same degree that it is impossible for an
> animal that is a cat and not a dog to be a dog and not a cat.
>
> You just aren't paying enough attention to the meaning of the words.

No. You are simply ignoring the actual definitions of 'halting problem'
and of 'halt decider'.

André

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