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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Two dozen people were simply wrong ---
Date: Sun, 2 Jun 2024 14:18:08 -0400
Organization: i2pn2 (i2pn.org)
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On 6/2/24 2:08 PM, olcott wrote:
> On 6/2/2024 12:55 PM, joes wrote:
>> Am Sun, 02 Jun 2024 10:02:54 -0500 schrieb olcott:
>>> On 6/2/2024 4:36 AM, joes wrote:
>>>> Am Sat, 01 Jun 2024 17:37:28 -0500 schrieb olcott:
>>>>> On 6/1/2024 5:30 PM, Richard Damon wrote:
>>>>>> On 6/1/24 5:27 PM, olcott wrote:
>>>>>>> On 6/1/2024 4:15 PM, Richard Damon wrote:
>>>>>>>> On 6/1/24 4:35 PM, olcott wrote:
>>>>>>>>> On 6/1/2024 3:29 PM, Richard Damon wrote:
>>>>>>>>>> On 6/1/24 12:46 PM, olcott wrote:
>>>>>>>>>>> On 6/1/2024 11:33 AM, Richard Damon wrote:
>>>>>>>>>>>> On 6/1/24 12:18 PM, olcott wrote:
>>>>>>>>>>>>> On 6/1/2024 11:08 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 6/1/24 11:58 AM, olcott wrote:
>>>>>>>>>>>>>>> On 6/1/2024 10:46 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 6/1/24 10:00 AM, olcott wrote:
>>>>
>>>>>>> Every DD correctly simulated by any HH of the infinite set of HH/DD
>>>>>>> pairs that match the above template never reaches past its own
>>>>>>> simulated line 03 in 1 to ∞ steps of correct simulation of DD by HH.
>>>>>>
>>>>>> But since the simulation was aborted,
>>>>>
>>>>> *The above never mentions anything about any simulation being aborted*
>>>> Not simulating an infinite number of steps of infinite recursion is
>>>> incorrect. You always forget this requirement: the simulation must be
>>>> complete.
>>>
>>> When HH correctly simulates N steps of DD it is incorrect to say that
>>> these N steps were incorrectly simulated.
>> The simulation is incorrect if it stops at that point and the simulated
>> machine is not in a final state, even if it was correct up to that point.
>> It also matters what steps where simulated, not only if each was correct.
>>
> 
> Introduction to the Theory of Computation, by Michael Sipser
> https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X/
> 
> On 10/13/2022 11:29:23 AM
> MIT Professor Michael Sipser agreed that this verbatim paragraph is correct
> (He has neither reviewed nor agreed to anything else in this paper)
> 
> <Professor Sipser agreed>
> 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.
> </Professor Sipser agreed>
> 
> 
>>>> What are the sets of HH and DD? I thought they were concrete machines.
>>>>
>>> The infinite set of every HH/DD pair where HH correctly simulates 1 or
>>> more steps of DD is the infinite set that I am referring to.
>> I see only a single DD. All H that stop simulating D before it reaches a
>> final state are already wrong.
>>
> 
> There are an infinite number of different HH/DD pairs specified by that
> template. One class of them simulates N steps and one class of them
> simulates ∞ steps. Some of them play a game of bingo before simulating
> any steps. Some of them play a game of chess after simulating N steps.
> 
> *IN NONE OF THESE CASES DOES DD CORRECTLY SIMULATED BY HH HALT*
> 

Which doesn't matter, since Halting is based on what DD(DD) itself does 
when run.

The class of DD that are simulated for a finite number of steps, and 
then HH aborts its simulation and returns 0, will all Halt when run, 
making HH's answer wrong.

The class of DD that are simulated for an infinite number of steps will 
be non-halting, but those HHs never give an answer, so are wrong.

The fact that we get different answers based on the HH proves that 
asking about the halting of the TEMPLATE DD is an invalid question, as 
it doesn't have a definable answer until paired with an HH, so we can 
only talk about the Halting of a given DD after it is paired to an HH, 
and while THAT HH can't give the right answer, other version of HH, that 
simulate enough longer or until reaching the end, when given THAT 
version (the one using the quicker HH) will be able to get the right answer.