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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Termination analyzer defined ---RICHARD IS WRONG !!!
Date: Sun, 19 May 2024 13:43:07 +0300
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On 2024-05-18 14:35:43 +0000, olcott said:

> On 5/18/2024 4:33 AM, Mikko wrote:
>> On 2024-05-17 15:53:33 +0000, olcott said:
>> 
>>> On 5/17/2024 3:58 AM, Mikko wrote:
>>>> On 2024-05-16 14:08:50 +0000, olcott said:
>>>> 
>>>>> On 5/16/2024 4:59 AM, Mikko wrote:
>>>>>> On 2024-05-15 14:52:01 +0000, olcott said:
>>>>>> 
>>>>>>> On 5/15/2024 2:53 AM, Mikko wrote:
>>>>>>>> On 2024-05-14 14:10:47 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 5/14/2024 4:28 AM, Mikko wrote:
>>>>>>>>>> On 2024-05-13 14:42:05 +0000, olcott said:
>>>>>>>>>> 
>>>>>>>>>>> On 5/13/2024 4:06 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-05-12 17:12:00 +0000, olcott said:
>>>>>>>>>>>> 
>>>>>>>>>>>>> On 5/12/2024 10:27 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-05-12 13:59:28 +0000, olcott said:
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> On 5/12/2024 3:45 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-05-11 16:35:48 +0000, olcott said:
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> On 5/11/2024 4:39 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>> On 2024-05-11 00:30:40 +0000, olcott said:
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> A termination analyzer is different than a halt decider in that it need
>>>>>>>>>>>>>>>>>>> not correctly determine the halt status of every input. For the purposes
>>>>>>>>>>>>>>>>>>> of this paper a termination analyzer only needs to correctly determine
>>>>>>>>>>>>>>>>>>> the halt status of one terminating input and one non-terminating input.
>>>>>>>>>>>>>>>>>>> The computer science equivalent would be a halt decider with a limited
>>>>>>>>>>>>>>>>>>> domain that includes at least one halting and one non-halting input.
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> From https://www.google.fi/search?q=termination+analysis and
>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Termination_analysis :
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> "In computer science, termination analysis is program analysis which 
>>>>>>>>>>>>>>>>>> attempts to determine whether the evaluation of a given program halts 
>>>>>>>>>>>>>>>>>> for each input. This means to determine whether the input program 
>>>>>>>>>>>>>>>>>> computes a total function."
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> So the term "termination analysis" is already defined. The derived term
>>>>>>>>>>>>>>>>>> "termination analyzer" means a performer of termination analysis. That
>>>>>>>>>>>>>>>>>> does not agree with the propsed defintion above so a differnt term
>>>>>>>>>>>>>>>>>> should be used.
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> That "termination analysis" is a know term that need not be defined
>>>>>>>>>>>>>>>>>> is demostrated e.g. by
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>    https://arxiv.org/pdf/2101.09783
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> which simply assumes that readers know (at least approximately) what
>>>>>>>>>>>>>>>>>> the term means.
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> You are doing a great job performing an honest review!
>>>>>>>>>>>>>>>>> So every time that Richard referred to a {termination analyzer} that
>>>>>>>>>>>>>>>>> ignores its inputs *Richard was WRONG*
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> More important is that you are wrong whenever you use "termination
>>>>>>>>>>>>>>>> analyser" for something that by the conventional meaning isn't.
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> A conventional termination analyzer is free to use any algorithm
>>>>>>>>>>>>>>> as long as it analyzes termination.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> It is not sufficient to analyse something about termination. The
>>>>>>>>>>>>>> conventional meaning is that a termination analyser does not say
>>>>>>>>>>>>>> "yes" unless the analysed program terminates with every possible
>>>>>>>>>>>>>> input.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>> 
>>>>>>>>>>>>> A specific program halts with every input is not at all the same
>>>>>>>>>>>>> thing as correctly analyzing every program with every input.
>>>>>>>>>>>> 
>>>>>>>>>>>> If you can't find out whether a program halts with every input even
>>>>>>>>>>>> after analyzing it with every input your analysis is not really
>>>>>>>>>>>> good enough for the purpose.
>>>>>>>>>>>> 
>>>>>>>>>>>> Anyway, if an analyzer can never tell whether a program terminates
>>>>>>>>>>>> with every possible input then it is not a termination analyzer.
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> My simple termination analyzer easily determines whether or not
>>>>>>>>>>> the limited class of programs that are in its domain halt on
>>>>>>>>>>> every input. For example D() only has three classes of inputs
>>>>>>>>>>> (a) Inputs that halt
>>>>>>>>>>> (b) Inputs that do not halt
>>>>>>>>>>> (c) itself.
>>>>>>>>>> 
>>>>>>>>>> If you can prove that it never gives a wrong "yes" answer
>>>>>>>>>> you can call it a "termination analyzer". Even better if
>>>>>>>>>> you can prove that it never gives a "yes" answer for an
>>>>>>>>>> invalid input.
>>>>>>>>>> 
>>>>>>>>>> However, it is not useful if it does not say "yes" about any useful
>>>>>>>>>> or interesting program.
>>>>>>>>>> 
>>>>>>>>>>> Because it is a termination analyzer it need not work for
>>>>>>>>>>> all programs. A partial halt decider with a limited domain
>>>>>>>>>>> seems to be the equivalent theory of computation terminology.
>>>>>>>>>> 
>>>>>>>>>> A partial halt decider is not a termination analyzer. Their input
>>>>>>>>>> spaces are distinct.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> It correctly determines the halt status YES or NO
>>>>>>>>> for a specific limited set of programs and ALL of
>>>>>>>>> the inputs to this limited infinite set of programs.
>>>>>>>> 
>>>>>>>> The important difference is that a partial halting decider takes
>>>>>>>> a pair (progam, input) for input but a halting analyzer takes
>>>>>>>> a singlet (program).
>>>>>>>> 
>>>>>>> 
>>>>>>> One can analyze whether a specific program will halt with a specific
>>>>>>> input.
>>>>>> 
>>>>>> However, there is no way to ensure that the answer is ever found.
>>>>>> 
>>>>> 
>>>>> For the C version and the Turing machine version of the halting problem
>>>>> template an answer <is> found.
>>>> 
>>>> That is a very restricted set of programs that are not very interesting.
>>>> 
>>> 
>>> If refuting the halting problem proofs is not very interesting then
>>> what is interesting?
>>> 
>>>> It is not sufficient that an answer must be given. There must be a
>>>> proof that the wrong answer is never given. For programs outside of
>>>> the domain and non-programs given as programs an answer that is
>>>> neither "yes" or "no" is permitted.
>>>> 
>>> 
>>> *Not at all. Not in the least little bit*
>>> For the H/D pairs comprising the halting problem counter-example all
>>> that needs be shown is that one of YES or NO <is> the correct answer.
>> 
>> That is trivial to show. What is hard is to tell which one is the
>> correct answer. Especially hard about D.
>> 
> 
> The halting problem proofs are intentionally formed to be isomorphic
> to the liar paradox such that both YES and NO are the wrong answer
> from every H.
> 
> Two PhD computer science professors wrote papers agreeing with this
> assessment. I have had very extensive direct talks with professor
> Hehner.
> 
> *Objective and Subjective Specifications* Eric C.R. Hehner 2017-7-10
> https://www.cs.toronto.edu/~hehner/OSS.pdf
> 
> *The Halting Paradox Bill Stoddart* 20 December 2017
> https://arxiv.org/pdf/1906.05340
> 
>>> I am not making an ALL KNOWING computer program that solves the halting
>>> problem. I am making a program that refutes the conventional halting
>>> problem proofs.
>> 
>> A program alone cannot refute a proof.
> 
> My proof is step-by-step

Proofs typically are but a program can only be a part of a step
of a proof. A statement that contains a program can be a step of
a proof but the step must containt something else, too, so that
it is a statement about something.

-- 
Mikko