Separability of Reachability Sets of Vector Addition Systems

Given two families of sets F and G, the separability problem of sets from a class G by sets from a class F asks whether for two given sets U, V in G there exists a set S in F such that U is included in S and V has an empty intersection with S.

We show that separability problem of reachability sets of Vector Addition Systems by both modular and unary sets is decidable.