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.

翻译：继最近考虑将线性方程式概括为无顺序数据矢量和定序数据矢量之后,我们进一步对数据矢量进行了归纳,这些矢量的功能来自未顺序数据组的K-元素子集,其功能来自整数矢量的矢量。这些概括式方程式自然出现在对矢量添加系统(或Petrii net)扩展的分析中,以便每个符号携带一组未顺序数据。我们显示,线性方形的非负内向内热分离性处于非确定性指数时间,而整数溶性则在多元时间。