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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Termination analyzer defined ---RICHARD IS WRONG !!!
Date: Thu, 16 May 2024 12:59:05 +0300
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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.

> This is especially important when the received view is that a
> specific program cannot possibly handle a specific input correctly.

It is easy to try a specifc program with a specific input and see
what happens, at least if the program terminates in a reasonble time.
Of course, if a program runs many years before it answers its correctness
is harder to determine.

-- 
Mikko