[PPL-devel] Z-polytopes in PPL

[Michael Classen]

Hello Pat,

I found something called (Non-)Relational Integral Grid-Polyhedron on
the PPL documentation site: http://www.cs.unipr.it/ppl/abstractions

This seems to be exactly the same as Z-Polytopes. And if you use
equalities instead of congruences, it also should be exactly the same
thing that we use: the integral image of a polytope under some affine
function.

Do you know if this "Integral Grid-Polyhedron" is accessable as a PPL
datatype easily?

ciao,
Michael

On Thu, Jun 18, 2009 at 3:56 PM, P M Hill<hill at comp.leeds.ac.uk> wrote:
> On Thu, 18 Jun 2009, Michael Classen wrote:
>
>> Hello,
>>
>> this might be a trivial question for some, but I just seem to have
>> problems with it:
>>
>> I want to adapt our internal LooPo interface to use PPL Grids instead
>> of Z-Polytopes. Now, Z-Polytopes were typically defined by a domain
>> (or inequality system) and an affine function, which is applied to
>> that domain (also alled Lattice).
>>
>> Now, in PPL, as far as I can see, you can only create Grids out of
>> inequality systems, congruence systems or Grid generators. Is there an
>> easy way (function, constructor) to generate a Grid from an inequality
>> system + affine function, like in the old Polylib?
>
> It appears as if you think that Grids can represent something akin to
> Z-polyhedra. This is not the case, the grids are just that "lattices". That
> is, only equalities and congruences are used to define a grid, not
> inequalities.
>
> The details about the domain are in the documentation of the PPL and also,
> in a more theoretical form, in:
> Proceedings of the 16th International Symposium on Logic-based Program
> Synthesis and Transformation (LOPSTR'06) (Venice, Italy, July 2006), volume
> 4407 of Lecture Notes in Computer Science, G. Puebla, Ed., pp. 219-235, 2007
> and available at
> http://www.cs.unipr.it/ppl/Documentation/bibliography
>
> What the PPL does also provide is a product domain as a templatic class
> (Partially_Reduced_Product). By instantiating the templatic arguments to
> Grid and C_Polyhedron (or NNC_Polyhedron), we can represent something like
> the Z-Polytopes in Polylib. There is a third templatic argument for this
> class for specifying a (partial) reduction procedure. If you let us know
> more exactly what you require for your Loopo interface, we can see if it is
> already available or if it would be straightforward to add the appropriate
> feature to the domain.
>
> Best wishes,
>  Pat
>
>
>>
>> thank you in advance!
>>
>> Greetings,
>> Michael
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>