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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 19:27:50 +0300
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On 2024-06-18 15:44:16 +0000, olcott said:

> On 6/18/2024 10:36 AM, Mikko wrote:
>> 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.
>> 
> 
> So maybe: *symbolically executes the LLVM program*
> means jumping up and down yelling and screaming?

Not a bad guess but not quite right either.

> AProVE does form its non-halting decision on the basis of the
> dynamic behavior of its input instead of any static analysis.

It is a kind of static analysis. The important diffrence is that
in a simulation there would be a specific input but AProVE considers
all possible inputs at the same time.

> *symbolically executes the LLVM program* means dynamic behavior
> and not static analysis.

It does not reproduce any specific example of the dynamic behaviour.

-- 
Mikko