Separability of Reachability Sets of Vector Addition Systems

Given two families of sets F and G, the F separability problem for G asks whether for two given sets U, V ∈ G there exists a set S ∈ F , such that U is included in S and V is disjoint with S. We consider two families of sets F : modular sets S ⊆ N, defined as unions of equivalence classes modulo some natural number n ∈ N, and unary sets. Our main result is decidability of modular and unary separability for the class G of reachability sets of Vector Addition Systems, Petri Nets, Vector Addition Systems with States, and for sections thereof.