[PPL-devel] Re: Convex hull

[Enrico Oliosi]

On Thu, 7 Oct 2004, Roberto Bagnara wrote:

> Enrico Oliosi wrote:
>> I analysed this program:
>>
>> BEGINPRG
>> Read(i);
>> j:=0;
>> IF (i >= 0) THEN {
>>           j:= i+2;
>>             [p1]={j=0; i>=0; j-i=2}
>>      } ELSE {
>>             j:= i;
>>             [p2]={j=0; -i>0; j-i=0}
>>         }
>> FI;
>> [1=0]
>> ENDPRG
>> 
>> when I done the convex-hull using:
>> 
>> [p1].poly_hull_assign_and_minimize([p2]);
>> 
>> the result has been the empty polyhedron ([1=0]).
>
> Dear Enrico,
>
> what you obtain is not surprising at all: since both p1 and p2
> are empty polyhedra, their poly-hull is the empty polyhedron.
>
>> (if I use the function [p1].poly_hull_assign([p2]) the poly_hull
>>  returns [p2]);
>
> This is still OK: the method poly_hull_assign() does not minimize
> the result and, since p1 is empty it simply gives you back p2.
>
> I think that the problem is elsewhere: the constraint `j=0'
> should not, I believe, be in p1 nor in p2.

OK but in Cousot&Halbwachs76 if I have a linear test C and P the
enter polyhedron P-true is defined as:

     P-true = P intersection C ( P-false = P intersecrion not(C) ).

If P is [j=0] and C is [i>=0] the intersection (P.intersection_assign_and_minimize(C);)
returns the Polyhedron P' = [j=0,i>=0]; the same holds for P_false ([j=0,i<0]).

What do I wrong? Probably I don't understand the guard rules very well....

Thanks,

     Enrico