Iterative arrays whose internal inter-cell communication is quantitatively restricted are investigated. The quantity of communication is measured by counting the number of uses of the links between cells. In particular, iterative arrays are studied where the maximum number of communications per cell occurring in accepting computations is drastically bounded by a constant number. Additionally, the iterative arrays have to work in realtime. We study the computational capacity of such devices. For example, a result is that a strict and dense hierarchy with respect to the constant number of communications exists. Due to their very restricted communication, the question arises whether the usually studied decidability problems such as, for example, emptiness, finiteness, inclusion, or equivalence become decidable for such devices. However, it can be shown that all such decidability questions remain undecidable even if only four communications per cell are allowed. Finally, the undecidability results are shown to hold as well for one-way and two-way cellular automata having at most four communications per cell.

研究了内部小区间通信受到定量限制的迭代阵列。通过计算小区之间链路的使用次数来衡量通信量。尤其是，研究了迭代数组，其中在接受计算中每个单元的最大通信数量以恒定的数量急剧限制。此外，迭代数组必须实时工作。我们研究了此类设备的计算能力。例如，结果是存在关于恒定数量的通信的严格且密集的层次结构。由于它们的非常受限的通信，因此出现了这样的问题，即通常研究的可确定性问题（例如，空性，有限性，包含性或等效性）对于这些设备是否可确定。然而，可以证明，即使每个小区只允许进行四个通信，所有这些可判定性问题仍然无法判定。最后，对于每个单元最多具有四个通信的单向和双向细胞自动机，不确定性结果也显示出来。