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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: V5 --- Professor Sipser
Date: Fri, 23 Aug 2024 10:59:55 +0300
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On 2024-08-23 03:53:14 +0000, olcott said:

> On 8/22/2024 10:11 PM, Richard Damon wrote:
>> On 8/22/24 10:54 PM, olcott wrote:
>>> On 8/22/2024 9:31 PM, Richard Damon wrote:
>>>> On 8/22/24 9:39 PM, olcott wrote:
>>>>> On 8/22/2024 8:26 PM, Richard Damon wrote:
>>>>>> On 8/22/24 9:21 PM, olcott wrote:
>>>>>>> On 8/22/2024 7:54 PM, Richard Damon wrote:
>>>>>>>> On 8/22/24 9:36 AM, olcott wrote:
>>>>>>>>> On 8/22/2024 8:21 AM, joes wrote:
>>>>>>>>>> Am Thu, 22 Aug 2024 07:59:59 -0500 schrieb olcott:
>>>>>>>>>>> On 8/22/2024 3:16 AM, Fred. Zwarts wrote:
>>>>>>>>>>>> Op 22.aug.2024 om 06:22 schreef olcott:
>>>>>>>>>>> 
>>>>>>>>>>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>>>>>>>>>       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.
>>>>>>>>>>> </MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>>>>>>>>> 
>>>>>>>>>>> We swap the word "determines" for "predicts"
>>>>>>>>>>> When we swap thew word "halt decider" for "termination analyzer" the
>>>>>>>>>>> above is translated from computer science into software engineering.
>>>>>>>>>>> The second half proves that this is the H that aborts that is making the
>>>>>>>>>>> prediction of the behavior of D when emulated by a hypothetical version
>>>>>>>>>>> of itself then never aborts.
>>>>>>>>>> 
>>>>>>>>>>>>> THIS EXACTLY MATCHES THE SIPSER APPROVED CRITERIA The finite HHH(DDD)
>>>>>>>>>>>>> emulates itself emulating DDD exactly once and this is sufficient for
>>>>>>>>>>>>> this HHH to predict what a different HHH(DDD) do that never aborted
>>>>>>>>>>>>> its emulation of its input.
>>>>>>>>>>>> But that different hypothetical HHH is a non-input.
>>>>>>>>>>> HHH is supposed to predict what the behavior of DDD would be if it did
>>>>>>>>>>> not abort its emulation of DDD that is what the words that Professor
>>>>>>>>>>> agreed to mean.
>>>>>>>>>> If IT didn’t abort DDD calling its aborting self.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> I don't know how you twist words to get that.
>>>>>>>>> HHH is required to predict the behavior of DDD
>>>>>>>>> as if every HHH had its abort code removed.
>>>>>>>> 
>>>>>>>> But that isn't the input, so that is just a LIE.
>>>>>>> 
>>>>>>> PREDICT HYPOTHETICAL BEHAVIOR
>>>>>> Nope, Predict the ACTUAL behavior.
>>>>>> 
>>>>>> You are just admitting you are lying about the
>>>>> 
>>>>> That is NOT what the words actually say.
>>>>> I hope you don't get condemned to Hell over this.
>>>>> 
>>>> 
>>>> Yes, it is, at least when you understand the TECHNICAL meaning of the 
>>>> words in Computation Theory.
>>> 
>>> Termination analyzers in software engineering are
>>> isomorphic to partial halt deciders in computer
>>> science you really can't get away with saying otherwise
>>> and not look foolish.
>> 
>> Then they must follow the same rules (or you are lying that they are 
>> isomoprhic).
>> 
>> Deciders of program behavior must be given PROGRAMS, which always 
>> contain ALL of the code used by it, thus for DDD, it includes the HHH 
>> that it calls.
>> 
> 
> It was ridiculous that you ever assumed otherwise.
> 
>> Incomplete descriptions that just don't contain everything are just incorrect.
>> 
>> Also, "Termination analyzers" are NOT the same thing as a Halt 
>> Deciders, as the term "Termination Analyzers" refer to something that 
>> decides if a given program will Halt on ALL POSSIBLE inputs, rather 
>> than the specific given input that a Halt Decider decides on.
>> 
> 
> So you don't know what "isomorphic" means.
> It does not mean identical in every respect.
> Maybe "functionally equivalent" is easy for you.

Structurally equivalent is probably better.

U and U' are said to be isomorphic if there is a higher order bijection
that maps every constituent x of U to the corresponding constituent x'
of U' so every constituent of U' is mapped from some constitient of U,
every function f in U to a function f' in U' so that for every x
in U the bijection maps f(x) to f'(x'), and for every predicate P in U
there is a corresponding predicate P' in U' so that for every x in U
P(x) <-> P'(x'), as well as similar correspondences for functions and
predicates of several arguments.

An isomorfism between U and U is called an automorphism of U.

-- 
Mikko