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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: Tue, 18 Jun 2024 07:46:13 -0500
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On 6/18/2024 2:44 AM, Mikko wrote:
> On 2024-06-17 12:51:15 +0000, olcott said:
> 
>> On 6/17/2024 2:10 AM, Mikko wrote:
>>> On 2024-06-16 12:59:02 +0000, olcott said:
>>>
>>>> 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.
>>>
>>> That would be just an example, not a definition. In particular, it does
>>> not tell about another being whether it can be called a "duck".
>>>
>>>> *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.
>>>
>>> A difference between AProVE and a partial halt decider is that the input
>>> to AProVE is only a program but not an input to that program but the
>>> input to a partial halt decider contains both.
>>>
>>>>>> *AProVE: Non-Termination Witnesses for C Programs*
>>>>>> https://link.springer.com/content/pdf/10.1007/978-3-030-99527-0_21.pdf
>>>
>>
>> AProVE is a kind of simulating termination analyzer.
> 
> Not really. It does not simulate.
> 

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)

>> H is a kind of simulating halt decider with a restricted domain.
>> [Simulating termination analyzers for dummies] makes these ideas
>> simpler.
> 

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