vector addition system

A VAS is a finite set $V\subseteq {\mathbb{Z}}^d$ for some $d\ge 1$

Let $V\subseteq {\mathbb{Z}}^d$ be a VAS. Given a vector $u\in {\mathbb{N}}^d$, the vector $u+v$ can be reached, in one transition, if $v\in V$ and $u+v\in {\mathbb{N}}^d$