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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D)
Date: Sun, 16 Jun 2024 07:59:02 -0500
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On 6/16/2024 4:15 AM, Mikko wrote:
> On 2024-06-15 13:24:45 +0000, olcott said:
> 
>> On 6/15/2024 7:33 AM, Mikko wrote:
>>> On 2024-06-15 11:34:39 +0000, joes said:
>>>
>>>> Am Fri, 14 Jun 2024 12:39:15 -0500 schrieb olcott:
>>>>> On 6/14/2024 10:54 AM, joes wrote:
>>>>>> Am Fri, 14 Jun 2024 08:15:52 -0500 schrieb olcott:
>>>>>>> On 6/14/2024 6:39 AM, Richard Damon wrote:
>>>>>>>> On 6/14/24 12:13 AM, olcott wrote:
>>>>>>>>> On 6/13/2024 10:44 PM, Richard Damon wrote:
>>>>>>>>>> On 6/13/24 11:14 PM, olcott wrote:
>>>>>>>>>>> On 6/13/2024 10:04 PM, Richard Damon wrote:
>>>>>>>>>>>> On 6/13/24 9:39 PM, olcott wrote:
>>>>>>>>>>>>> On 6/13/2024 8:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 6/13/24 11:32 AM, olcott wrote:
>>>>
>>>>>>> When H and D have a pathological relationship to each other then
>>>>>>> H(D,D) is not being asked about the behavior of D(D). H1(D,D) has no
>>>>>>> such pathological relationship thus D correctly simulated by H1 
>>>>>>> is the
>>>>>>> behavior of D(D).
>>>> What is H1 asked?
>>>>>> H is asked whether its input halts, and by definition should give the
>>>>>> (right) answer for every input.
>>>>> If we used that definition of decider then no human ever decided
>>>>> anything because every human has made at least one mistake.
>>>> Yes. Humans are not machines.
>>>>> I use the term "termination analyzer" as a close fit. The term partial
>>>>> halt decider is more accurate yet confuses most people.
>>>
>>> Olcott has used the term "termination analyzer", though whether he knows
>>> what it means is unclear.
>>>
>>
>> To prove (non-)termination of a C program, AProVE uses the Clang 
>> compiler [7] to translate it to the intermediate representation of the 
>> LLVM framework [15]. Then AProVE symbolically executes the LLVM 
>> program and uses abstraction to obtain a finite symbolic execution 
>> graph (SEG) containing all possible program runs.
> 
> AProVE is a particular attempt, not a defintion.
> 

If you say: What is a duck? and I point to a duck that
*is* what a duck is.

*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.
https://en.wikipedia.org/wiki/Termination_analysis

I pointed out AProVE because it is essentially a simulating
halt decider with a limited domain.

>> *AProVE: Non-Termination Witnesses for C Programs*
>> https://link.springer.com/content/pdf/10.1007/978-3-030-99527-0_21.pdf
>>
>>> The main difference is that a halt decider or partial halt decider takes
>>> descriptions of both a Turing machine (or other program) and an input 
>>> and
>>> determines whether that machine halts with that input
>>
>> H(D,D) is only required to get this one input correctly thus H is
>> a halt decider with a domain restricted to D.
> 
> Nevertheless, it takes both the program and its input inputs.
> 

And both the program and its input proves that H(D,D) is not and cannot
report on the behavior of the directly executed D(D).

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer