1
For technical reasons, the PAF compiler deals only with convex D domains.
2
We acknowledge that this definition lacks in precision. It should be completed by complexity considerations: the ``size'' of the result should not increase, or, at least, increase more slowly than the total size of the arguments.
3
Our DFG constructor may find non convex domains but the handling of such cases is left for future work.
4
A strongly connected system is a system whose graph is strongly connected. In the same way a strong component of a system is the set of variables from a strong component of its graph
5
More complete proofs for the theorems of this section can be found in [RF:97].
6
From the technical point of view, this means that the sub-spaces C and D are supposed to be expressed using vectors of the same size. That is not a restriction since one may always consider a vector of size n as a vector of Zn+n' by adding n' zeroes.