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I have hardly ever known a mathematician who was capable of reasoning. -- Plato


devel / comp.theory / Re: Halt deciders

SubjectAuthor
* Halt decidersFred. Zwarts
+- Halt decidersPaul N
+* Halt deciderswij
|`- Halt decidersolcott
+* Halt decidersMikko
|+- Halt decidersolcott
|`* Halt decidersAndy Walker
| `- Halt decidersolcott
+* Halt decidersDennis Bush
|`* Halt decidersolcott
| `* Halt decidersDennis Bush
|  `* Halt decidersolcott
|   `* Halt decidersDennis Bush
|    `* Halt decidersolcott
|     `* Halt decidersDennis Bush
|      +* Halt decidersolcott
|      |`* Halt decidersDennis Bush
|      | `* Halt decidersolcott
|      |  `* Halt decidersDennis Bush
|      |   `* Halt decidersolcott
|      |    `* Halt decidersDennis Bush
|      |     `* Halt decidersolcott
|      |      +* Halt decidersDennis Bush
|      |      |`* Halt decidersolcott
|      |      | +* Halt decidersMr Flibble
|      |      | |+- Halt deciders [ Does Ben agree? ]olcott
|      |      | |`- Halt deciders [ Does Ben agree ? ]olcott
|      |      | `* Halt decidersDennis Bush
|      |      |  `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |   `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |    `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |     `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |      `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |       `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |        `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |         `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |          `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |           `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |            `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |             `* Halt deciders [ Does Ben agree ? ]Dennis Bush
|      |      |              `* Halt deciders [ Does Ben agree ? ]olcott
|      |      |               `- Halt deciders [ Does Ben agree ? ]Richard Damon
|      |      `- Halt decidersPython
|      `* Halt decidersBen Bacarisse
|       +- Halt decidersMr Flibble
|       +- Halt deciders [ Ben has no rebuttal for this ]olcott
|       `- Halt deciders [ Ben uses rhetoric when he has no reasoning ]olcott
`* Halt decidersolcott
 `* Halt decidersFred. Zwarts
  +- Halt decidersSergi o
  `* Halt decidersolcott
   `* Halt decidersFred. Zwarts
    +* Halt decidersPaul N
    |`- Halt decidersolcott
    `* Halt decidersolcott
     `* Halt decidersFred. Zwarts
      `* Halt decidersolcott
       `* Halt decidersFred. Zwarts
        `* Halt decidersolcott
         +* Halt decidersFred. Zwarts
         |`* Halt decidersolcott
         | +- Halt decidersPython
         | `* Halt decidersFred. Zwarts
         |  `* Halt decidersolcott
         |   `* Halt decidersMr Flibble
         |    `* Halt decidersolcott
         |     `* Halt decidersMr Flibble
         |      `* Halt decidersolcott
         |       `* Halt decidersMikko
         |        +- Halt decidersolcott
         |        `* Halt decidersolcott
         |         `* Halt decidersMikko
         |          +* Halt decidersRichard Damon
         |          |`* Halt decidersolcott
         |          | `* Halt decidersRichard Damon
         |          |  `* Halt decidersolcott
         |          |   `* Halt decidersRichard Damon
         |          |    `- Halt decidersolcott
         |          `* Halt decidersolcott
         |           `* Halt decidersPython
         |            `- Halt decidersolcott
         `* Halt deciderswij
          `* Halt decidersolcott
           `- Halt decidersPython

Pages:1234
Re: Halt deciders

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Subject: Re: Halt deciders
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sat, 22 Oct 2022 14:21 UTC

On 10/22/22 10:13 AM, Mikko wrote:
> On 2022-10-22 12:24:23 +0000, olcott said:
>
>> On 10/22/2022 3:51 AM, Mikko wrote:
>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>
>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>
>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>
>>>> One would think so until one looked at all of the details.
>>>
>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>> then H is not a halt decider.
>>>
>>> Mikko
>>>
>>
>> Professor Sipser seems to disagree because an execution trace of the
>> D simulated by H would never stop running unless its simulation has
>> been aborted. By ignoring these details one simply remains ignorant.
>
> It may seem so if one ovelooks important details. When one considers
> those details one can see that he doesn't disagree.
>
> Mikko
>

Yes, "Small things", like being "Correct".

Re: Halt deciders

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 09:44:32 -0500
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 by: olcott - Sat, 22 Oct 2022 14:44 UTC

On 10/22/2022 9:13 AM, Mikko wrote:
> On 2022-10-22 12:24:23 +0000, olcott said:
>
>> On 10/22/2022 3:51 AM, Mikko wrote:
>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>
>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>
>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>
>>>> One would think so until one looked at all of the details.
>>>
>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>> then H is not a halt decider.
>>>
>>> Mikko
>>>
>>
>> Professor Sipser seems to disagree because an execution trace of the
>> D simulated by H would never stop running unless its simulation has
>> been aborted. By ignoring these details one simply remains ignorant.
>
> It may seem so if one ovelooks important details. When one considers
> those details one can see that he doesn't disagree.
>
> Mikko
>

Both Ben and another software engineer agree that Sipser_H does
correctly compute the halt status of Sipser_D according to the Sipser
approved criteria.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: Halt deciders

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 09:49:11 -0500
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 by: olcott - Sat, 22 Oct 2022 14:49 UTC

On 10/22/2022 9:21 AM, Richard Damon wrote:
> On 10/22/22 10:13 AM, Mikko wrote:
>> On 2022-10-22 12:24:23 +0000, olcott said:
>>
>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>
>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>
>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>
>>>>> One would think so until one looked at all of the details.
>>>>
>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>> then H is not a halt decider.
>>>>
>>>> Mikko
>>>>
>>>
>>> Professor Sipser seems to disagree because an execution trace of the
>>> D simulated by H would never stop running unless its simulation has
>>> been aborted. By ignoring these details one simply remains ignorant.
>>
>> It may seem so if one ovelooks important details. When one considers
>> those details one can see that he doesn't disagree.
>>
>> Mikko
>>
>
> Yes, "Small things", like being "Correct".

Both Ben and another software engineer agree that Sipser_H does
correctly compute the halt status of Sipser_D according to the Sipser
approved criteria.

*Ben flatly said that you are applying the wrong criteria*

On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> Richard Damon <Richard@Damon-Family.org> writes:
>> The correct simulation is the correct simulation who
>> ever does it, and since D will halt when run, the correct
>> simulation of D will halt.
>
> Right, but that's not the criterion that PO is using, is it?

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: Halt deciders

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Newsgroups: comp.theory
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 16:50:42 +0200
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 by: Python - Sat, 22 Oct 2022 14:50 UTC

Deadly Sinner Peter Olcott wrote:
> On 10/22/2022 9:13 AM, Mikko wrote:
>> On 2022-10-22 12:24:23 +0000, olcott said:
>>
>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>
>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>
>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>
>>>>> One would think so until one looked at all of the details.
>>>>
>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>> then H is not a halt decider.
>>>>
>>>> Mikko
>>>>
>>>
>>> Professor Sipser seems to disagree because an execution trace of the
>>> D simulated by H would never stop running unless its simulation has
>>> been aborted. By ignoring these details one simply remains ignorant.
>>
>> It may seem so if one ovelooks important details. When one considers
>> those details one can see that he doesn't disagree.
>>
>> Mikko
>>
>
> Both Ben and another software engineer agree that Sipser_H does
> correctly compute the halt status of Sipser_D according to the Sipser
> approved criteria.
>

https://www.youtube.com/watch?v=E8zZLB3mW5o

Re: Halt deciders

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 by: Richard Damon - Sat, 22 Oct 2022 15:12 UTC

On 10/22/22 10:49 AM, olcott wrote:
> On 10/22/2022 9:21 AM, Richard Damon wrote:
>> On 10/22/22 10:13 AM, Mikko wrote:
>>> On 2022-10-22 12:24:23 +0000, olcott said:
>>>
>>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>>
>>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>>
>>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>>
>>>>>> One would think so until one looked at all of the details.
>>>>>
>>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>>> then H is not a halt decider.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> Professor Sipser seems to disagree because an execution trace of the
>>>> D simulated by H would never stop running unless its simulation has
>>>> been aborted. By ignoring these details one simply remains ignorant.
>>>
>>> It may seem so if one ovelooks important details. When one considers
>>> those details one can see that he doesn't disagree.
>>>
>>> Mikko
>>>
>>
>> Yes, "Small things", like being "Correct".
>
> Both Ben and another software engineer agree that Sipser_H does
> correctly compute the halt status of Sipser_D according to the Sipser
> approved criteria.
>

Look at the words used.

Define "If" and "Correct".

> *Ben flatly said that you are applying the wrong criteria*
>
> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> > Richard Damon <Richard@Damon-Family.org> writes:
> >> The correct simulation is the correct simulation who
> >> ever does it, and since D will halt when run, the correct
> >> simulation of D will halt.
> >
> > Right, but that's not the criterion that PO is using, is it?
>

So you agree that you aren't using the right criteria?

Isn't that the conclusion of me being incorrect to apply the
definitional criteria for your analysis?

Re: Halt deciders

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From: none...@beez-waxes.com (olcott)
Newsgroups: comp.theory,sci.logic
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 10:25:34 -0500
Organization: Aioe.org NNTP Server
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 by: olcott - Sat, 22 Oct 2022 15:25 UTC

On 10/22/2022 9:50 AM, Python wrote:
> Deadly Sinner Peter Olcott wrote:
>> On 10/22/2022 9:13 AM, Mikko wrote:
>>> On 2022-10-22 12:24:23 +0000, olcott said:
>>>
>>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>>
>>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>>
>>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>>
>>>>>> One would think so until one looked at all of the details.
>>>>>
>>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>>> then H is not a halt decider.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> Professor Sipser seems to disagree because an execution trace of the
>>>> D simulated by H would never stop running unless its simulation has
>>>> been aborted. By ignoring these details one simply remains ignorant.
>>>
>>> It may seem so if one ovelooks important details. When one considers
>>> those details one can see that he doesn't disagree.
>>>
>>> Mikko
>>>
>>
>> Both Ben and another software engineer agree that Sipser_H does
>> correctly compute the halt status of Sipser_D according to the Sipser
>> approved criteria.
>>
>
> https://www.youtube.com/watch?v=E8zZLB3mW5o

On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> D(D) would not halt unless H stops the simulation.
> H /can/ correctly determine this silly criterion (in this one case)

*This is the "silly" criterion that Ben is referring to*

On 10/17/2022 12:11 AM, olcott wrote:
> *Professor Sipser has agreed to these verbatim words* (and no more)
> If simulating halt decider H correctly simulates its input D until H
> correctly determines that its simulated D would never stop running
> unless aborted then H can abort its simulation of D and correctly
> report that D specifies a non-halting sequence of configurations.
>

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Halt deciders

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,sci.logic
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 10:29:08 -0500
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 by: olcott - Sat, 22 Oct 2022 15:29 UTC

On 10/22/2022 10:12 AM, Richard Damon wrote:
> On 10/22/22 10:49 AM, olcott wrote:
>> On 10/22/2022 9:21 AM, Richard Damon wrote:
>>> On 10/22/22 10:13 AM, Mikko wrote:
>>>> On 2022-10-22 12:24:23 +0000, olcott said:
>>>>
>>>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>>>
>>>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>>>
>>>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>>>
>>>>>>> One would think so until one looked at all of the details.
>>>>>>
>>>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>>>> then H is not a halt decider.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> Professor Sipser seems to disagree because an execution trace of the
>>>>> D simulated by H would never stop running unless its simulation has
>>>>> been aborted. By ignoring these details one simply remains ignorant.
>>>>
>>>> It may seem so if one ovelooks important details. When one considers
>>>> those details one can see that he doesn't disagree.
>>>>
>>>> Mikko
>>>>
>>>
>>> Yes, "Small things", like being "Correct".
>>
>> Both Ben and another software engineer agree that Sipser_H does
>> correctly compute the halt status of Sipser_D according to the Sipser
>> approved criteria.
>>
>
> Look at the words used.
>
> Define "If" and "Correct".
>
>> *Ben flatly said that you are applying the wrong criteria*
>>
>> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
>>  > Richard Damon <Richard@Damon-Family.org> writes:
>>  >> The correct simulation is the correct simulation who
>>  >> ever does it, and since D will halt when run, the correct
>>  >> simulation of D will halt.
>>  >
>>  > Right, but that's not the criterion that PO is using, is it?
>>
>
> So you agree that you aren't using the right criteria?

On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> D(D) would not halt unless H stops the simulation.
> H /can/ correctly determine this silly criterion (in this one case)

*This is the "silly" criterion that Ben is referring to*

On 10/17/2022 12:11 AM, olcott wrote:
> *Professor Sipser has agreed to these verbatim words* (and no more)
> If simulating halt decider H correctly simulates its input D until H
> correctly determines that its simulated D would never stop running
> unless aborted then H can abort its simulation of D and correctly
> report that D specifies a non-halting sequence of configurations.
>

I am using the above validated criteria.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: Halt deciders

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 by: Richard Damon - Sat, 22 Oct 2022 16:05 UTC

On 10/22/22 11:29 AM, olcott wrote:
> On 10/22/2022 10:12 AM, Richard Damon wrote:
>> On 10/22/22 10:49 AM, olcott wrote:
>>> On 10/22/2022 9:21 AM, Richard Damon wrote:
>>>> On 10/22/22 10:13 AM, Mikko wrote:
>>>>> On 2022-10-22 12:24:23 +0000, olcott said:
>>>>>
>>>>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>>>>
>>>>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>>>>
>>>>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>>>>
>>>>>>>> One would think so until one looked at all of the details.
>>>>>>>
>>>>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>>>>> then H is not a halt decider.
>>>>>>>
>>>>>>> Mikko
>>>>>>>
>>>>>>
>>>>>> Professor Sipser seems to disagree because an execution trace of the
>>>>>> D simulated by H would never stop running unless its simulation has
>>>>>> been aborted. By ignoring these details one simply remains ignorant.
>>>>>
>>>>> It may seem so if one ovelooks important details. When one considers
>>>>> those details one can see that he doesn't disagree.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> Yes, "Small things", like being "Correct".
>>>
>>> Both Ben and another software engineer agree that Sipser_H does
>>> correctly compute the halt status of Sipser_D according to the Sipser
>>> approved criteria.
>>>
>>
>> Look at the words used.
>>
>> Define "If" and "Correct".
>>
>>> *Ben flatly said that you are applying the wrong criteria*
>>>
>>> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
>>>  > Richard Damon <Richard@Damon-Family.org> writes:
>>>  >> The correct simulation is the correct simulation who
>>>  >> ever does it, and since D will halt when run, the correct
>>>  >> simulation of D will halt.
>>>  >
>>>  > Right, but that's not the criterion that PO is using, is it?
>>>
>>
>> So you agree that you aren't using the right criteria?
>
> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> > D(D) would not halt unless H stops the simulation.
> > H /can/ correctly determine this silly criterion (in this one case)
>
> *This is the "silly" criterion that Ben is referring to*
>
> On 10/17/2022 12:11 AM, olcott wrote:
> > *Professor Sipser has agreed to these verbatim words* (and no more)
> > If simulating halt decider H correctly simulates its input D until H
> > correctly determines that its simulated D would never stop running
> > unless aborted then H can abort its simulation of D and correctly
> > report that D specifies a non-halting sequence of configurations.
> >
>
> I am using the above validated criteria.
>
>

Are you? What does *If* and *Correct* mean?

Re: Halt deciders

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From: none...@beez-waxes.com (olcott)
Newsgroups: comp.theory,sci.logic
Subject: Re: Halt deciders
Date: Sat, 22 Oct 2022 11:21:52 -0500
Organization: Aioe.org NNTP Server
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 by: olcott - Sat, 22 Oct 2022 16:21 UTC

On 10/22/2022 11:05 AM, Richard Damon wrote:
> On 10/22/22 11:29 AM, olcott wrote:
>> On 10/22/2022 10:12 AM, Richard Damon wrote:
>>> On 10/22/22 10:49 AM, olcott wrote:
>>>> On 10/22/2022 9:21 AM, Richard Damon wrote:
>>>>> On 10/22/22 10:13 AM, Mikko wrote:
>>>>>> On 2022-10-22 12:24:23 +0000, olcott said:
>>>>>>
>>>>>>> On 10/22/2022 3:51 AM, Mikko wrote:
>>>>>>>> On 2022-10-21 14:12:21 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 10/21/2022 8:59 AM, Mr Flibble wrote:
>>>>>>>>
>>>>>>>>>> If D(D) halts then H(D,D) should return a decision of halts (1).
>>>>>>>>
>>>>>>>>> One would think so until one looked at all of the details.
>>>>>>>>
>>>>>>>> The relevant detail here is that if D(D) halts and H(D,D) says "no"
>>>>>>>> then H is not a halt decider.
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> Professor Sipser seems to disagree because an execution trace of the
>>>>>>> D simulated by H would never stop running unless its simulation has
>>>>>>> been aborted. By ignoring these details one simply remains ignorant.
>>>>>>
>>>>>> It may seem so if one ovelooks important details. When one considers
>>>>>> those details one can see that he doesn't disagree.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> Yes, "Small things", like being "Correct".
>>>>
>>>> Both Ben and another software engineer agree that Sipser_H does
>>>> correctly compute the halt status of Sipser_D according to the
>>>> Sipser approved criteria.
>>>>
>>>
>>> Look at the words used.
>>>
>>> Define "If" and "Correct".
>>>
>>>> *Ben flatly said that you are applying the wrong criteria*
>>>>
>>>> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
>>>>  > Richard Damon <Richard@Damon-Family.org> writes:
>>>>  >> The correct simulation is the correct simulation who
>>>>  >> ever does it, and since D will halt when run, the correct
>>>>  >> simulation of D will halt.
>>>>  >
>>>>  > Right, but that's not the criterion that PO is using, is it?
>>>>
>>>
>>> So you agree that you aren't using the right criteria?
>>
>> On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
>>  > D(D) would not halt unless H stops the simulation.
>>  > H /can/ correctly determine this silly criterion (in this one case)
>>
>> *This is the "silly" criterion that Ben is referring to*
>>
>> On 10/17/2022 12:11 AM, olcott wrote:
>>  > *Professor Sipser has agreed to these verbatim words* (and no more)
>>  > If simulating halt decider H correctly simulates its input D until H
>>  > correctly determines that its simulated D would never stop running
>>  > unless aborted then H can abort its simulation of D and correctly
>>  > report that D specifies a non-halting sequence of configurations.
>>  >
>>
>> I am using the above validated criteria.
>>
>>
>
> Are you? What does *If* and *Correct* mean?

On 10/17/2022 10:23 AM, Ben Bacarisse wrote:
> D(D) would not halt unless H stops the simulation.
> H /can/ correctly determine this silly criterion (in this one case)

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

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