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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D)
Date: Tue, 18 Jun 2024 18:36:19 +0300
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On 2024-06-18 12:46:13 +0000, olcott said:

> 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*

I.e., does not simulate.

> 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.

-- 
Mikko