Separability of Reachability Sets of Vector Addition Systems
Résumé
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 d , defined as unions of equivalence classes modulo some natural number n ∈ N, and unary sets, which extend modular sets by requiring equality below a threshold n, and equivalence modulo n above n. Our main result is decidability of modular and unary separability for the class G of reachability sets of Vector Addition Systems,
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