[PPL-devel] some questions regarding PPL

[Roberto Bagnara]

On 02/12/2016 02:00 PM, Bishoksan Kafle wrote:
> 
> On Feb 12, 2016, at 8:03 AM, Roberto Bagnara <bagnara at cs.unipr.it> wrote:
> 
>> On 02/11/2016 09:17 PM, Bishoksan Kafle wrote:
>>>
>>> On Feb 11, 2016, at 8:05 AM, Roberto Bagnara <bagnara at cs.unipr.it <mailto:bagnara at cs.unipr.it>> wrote:
>>>
>>>>>
>>>>> 2. In the article
>>>>> (http://bugseng.com/products/ppl/documentation/BagnaraRZH02.pdf),
>>>>> you mentioned that poly_hull_assign is different from
>>>>> upper_bound_assign for Polyhedra
>>>>
>>>> Where exactly do you read that?
>>>
>>> Sorry I wanted to ask the difference between poly-hull and convex-hull. Please ignore my previous question.
>>
>> The convex polyhedral hull of a set of convex polyhedra P is the smallest
>> convex polyhedron that contains all members of P.
>>
>> The convex hull of a set of convex polyhedra P is the smallest
>> convex set that contains all members of P.
>>
>> There exists P such that convex_polyhedral_hull(P) != convex_hull(P).
>> For instance, take P = { p1, p2 } where:
>>
>>  p1 = { (x, y) in R^2 | x = 0 },
>>  p2 = { (x, y) in R^2 | x = 0, y = 1 }.
>>
>> We have that (1, 1) belongs to convex_polyhedral_hull(P)
>> but (1, 1) does *not* belong to convex_hull(P).
> 
> I see your point, but do you mean   
> 	p2 = { (x, y) in R^2 | x = 1, y = 1 } 
> instead of  
> 	p2 = { (x, y) in R^2 | x = 0, y = 1 }?

Sorry, I mistyped it by swapping x and y in p2:
I meant

  p1 = { (x, y) in R^2 | x = 0 },
  p2 = { (x, y) in R^2 | x = 1, y = 0 }.

We have that (1, 1) belongs to convex_polyhedral_hull(P)
but (1, 1) does *not* belong to convex_hull(P).

Kind regards,

   Roberto

-- 
     Prof. Roberto Bagnara

Applied Formal Methods Laboratory - University of Parma, Italy
mailto:bagnara at cs.unipr.it
                              BUGSENG srl - http://bugseng.com
                              mailto:roberto.bagnara at bugseng.com