[PPL-devel] Fwd: Info on PPL

[Enea Zaffanella]

Giorgio Delzanno wrote:
 > Enea,
 > together with Ahmed Rezine (in cc) we'd like to use PPL for defining a
 > sort of "extrapolation" method
 > (to be applied as a subroutine of a verification process).
 > To give you an example, suppose we compute (forward) a sequence of
 > tuples of values
 > (valuation of variables)  like (0,0) (1,1) (2,2)...
 >  From this we would like to "extrapolate" the constraint X=Y without
 > fixing in advance the
 > shape of  equations (e.g. Y=MX+Q) we have to consider.
 >
 > Is there some kind of acceleration/widening that can be applied in this
 > case?
 > Thanks in advance,
 > Giorgio
 > ps: ... eventually, we started using PPL  :>
 >
 >

Giorgio,

the simple case above can be modeled using several (weakly) relational 
abstract domains, such as polyhedra, octagonal shapes and BD shapes, and 
probably using several variations of the standard widening of Cousot and 
Halbwachs.

Practically, suppose that you choose topologically closed polyhedra 
(i.e., class C_Polyhedron in the C++ interface of the PPL), using the 
standard widening (i.e., method H79_widening_assign in the C++ interface 
of the PPL). Let P_0, P_1, ..., P_i, ... be the sequence of polyhedra, 
where each P_i is a 2-dim polyhedron defined by the constraints
   { x = i, y = i }.
Then, you will end up computing the sequence of Q_i where

   Q_0 := P_0 = { x = 0, y = 0 };

   Q_1 := hull_1.H79_widening_assign(Q_0) = { x = y, y >= 0 },
     where
      hull_1 := the poly-hull of P_1 and Q_0
              = { x = y, 0 <= y <= 1 }

   Q_2 := hull_2.H79_widening_assign(Q_1) = Q_1 (fixpoint)
     where
      hull_2 := the poly-hull of P_2 and Q_1
              = { x = y, 0 <= y <= 2 }

Hope this is what you really meant.

Cheers,
Enea.

P.S.: Please, direct all PPL-related messages to ppl-devel at cs.unipr.it.