Let G be a group and A a set. A cellular automaton (CA) τ over $A^G$ is von Neumann regular (vN-regular) if there exists a CA σ over $A^G$ such that $\tau \sigma \tau =\tau$, and in such case, σ is called a weak generalised inverse of τ. In this paper, we investigate the vN-regularity of various kinds of CA. First, we establish that, except for trivial cases, there are always CA that are not vN-regular. Second, we obtain a partial classification of elementary vN-regular CA over ${\{0,1\}}^{\mathbb{Z}}$ by taking advantage of some symmetries among them. Next, when A and G are both finite, we obtain a full characterisation of vN-regular CA over $A^G$. Finally, we study vN-regular linear CA when $A=V$ is a vector space over and characterise them in certain situations.

设G为一组，A为一组。元胞自动机（CA）τ超过${\mathrm{一种}}^G$是冯·诺依曼定期（VN-常规）如果存在CA σ过${\mathrm{一种}}^G$ 这样 $\tau \sigma \tau =\tau$，在这种情况下，σ称为τ的弱广义逆。在本文中，我们研究了各种CA的vN正则性。首先，我们确定，除了琐碎的情况外，总是存在不是vN规则的CA。其次，我们获得了基本vN-常规CA的部分分类${\{0，\mathrm{1个}\}}^{\mathbb{ž}}$通过利用其中的一些对称性。接下来，当A和G都是有限的时，我们获得vN-regular CA的完整特征。${\mathrm{一种}}^G$。最后，我们研究vN-regular线性CA$\mathrm{一种}=V$ 是向量空间，并在某些情况下将其表征。