Following a recently considered generalisation of linear equations to unordered-data vectors and to ordered-data vectors, we perform a further generalisation to data vectors that are functions from k-element subsets of the unordered-data set to vectors of integer numbers. 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.

@article{paperbot1638,
  title = {Linear equations for unordered data vectors in $[D]^k\to{}Z^d$},
  author = {Piotr Hofman and Jakub Różycki},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 4},
  year = {2022},
  doi = {10.46298/lmcs-18(4:11)2022}
}