A natural way to interpret a cellular automaton (CA) is as a mechanism that computes, in a distributed way, some function f. In other words, from a computer science point of view, CAs can be seen as distributed systems where the cells of the CAs are nodes of a network linked by communication channels. A classic measure of efficiency in such distributed systems is the number of bits exchanged during the computation process. A typical approach is to look for bottlenecks: channels through which the nature of the function f forces the exchange of a significant number of bits. In practice, a widely used way to understand such congestion phenomena is to partition the system into two subsystems and try to find bounds for the number of bits that must pass through the channels that join them. Finding these bounds is the focus of communication complexity theory. Measuring the communication complexity of some problems induced by a CA \(\phi\) turned out to be tremendously useful to give clues regarding the intrinsic universality of \(\phi\) (a CA is said to be intrinsically universal if it is capable of emulating any other). In fact, there exist particular problems \(\mathrm {P}\)’s for which the following key property holds: if \(\phi\) is intrinsically universal, then the communication complexity of \(\mathrm {P}(\phi )\) must be maximal. In this tutorial, we intend to explain the connections that were found, through a series of papers, between intrinsic universality and communication complexity in CAs.

解释元胞自动机 (CA) 的一种自然方式是作为一种以分布式方式计算某个函数f 的机制。换句话说，从计算机科学的角度来看，CA 可以被视为分布式系统，其中 CA 的单元是通过通信通道链接的网络节点。在这种分布式系统中，一个经典的效率衡量标准是计算过程中交换的比特数。一个典型的方法是寻找瓶颈：函数f的性质强制交换大量比特所通过的通道。在实践中，理解这种拥塞现象的一种广泛使用的方法是将系统划分为两个子系统，并尝试找到必须的比特数的界限。通过加入他们的渠道。寻找这些界限是通信复杂性理论的重点。测量由 CA \(\phi\)引起的某些问题的通信复杂性对于提供有关\(\phi\)内在普遍性的线索非常有用（如果 CA 能够模仿任何其他）。事实上，存在以下关键性质的特殊问题\(\mathrm {P}\)：如果\(\phi\)本质上是通用的，那么\(\mathrm {P}( \phi )\)必须是最大的。在本教程中，我们打算通过一系列论文解释在 CA 中的内在普遍性和通信复杂性之间发现的联系。