Linear equations for unordered data vectors

Following a recently considered generalisation of linear equations to unordered-data vectors and to ordered-data vectors, we perform a further generalisation to k-element-sets-of-unordered-data vectors. These generalised equations naturally appear in the analysis of vector addition systems (or Petri nets) extended so that each token carries a set of unordered data. We show that nonnegative-integer solvability of linear equations is in nondeterministic-exponential-time while integer solvability is in polynomial-time.