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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: Sat, 15 Jun 2024 08:24:45 -0500
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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: 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.

> but a termination
> analyzer takes only the dexcription of a Turing machine (or other program)
> and attempts to determine whether that machine halts with every input.
> The term "analyzer" instead "decider" indicates that it may fail to
> determine on some inputs 

Yes that is the distinction that I intend.

> and that it may produce additional information
> that may be useful. The intent is to create termination analyzers that
> are useful for practical purposes.
> 

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