Linear equations for unordered data vectors in $[D]^k\to{}Z^d$

Abstract

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.

Keywords

• computer science - computational complexity
• computer science - formal languages and automata theory
• computer science - symbolic computation
• 68q85
• f.4.2
• g.2.2
• f.3.1