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.

中文翻译：

---

无序数据向量的线性方程

在最近考虑将线性方程推广到无序数据向量和有序数据向量之后，我们对无序数据向量的 k 元素集进行了进一步的推广。这些广义方程自然出现在向量加法系统（或 Petri 网）的分析中，扩展后每个标记携带一组无序数据。我们表明，线性方程的非负整数可解性处于非确定指数时间，而整数可解性处于多项式时间。