We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite sequence of synchronous rounds. The problem is shown to be decidable in LogSpace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. When restricted to the appropriate families of graphs, these forgetful automata are equivalent to classical finite word automata, but strictly more expressive than finite tree automata. On the other hand, we also show that the emptiness problem is undecidable in general. This already holds for two heavily restricted classes of distributed automata: those that reject immediately if they receive more than one message per round, and those whose state diagram must be acyclic except for self-loops. Additionally, to demonstrate the flexibility of distributed automata in simulating different models of computation, we provide a characterization of constraint satisfaction problems by identifying a class of automata with exactly the same computational power.

我们研究了三类分布式自动机的空性问题的可判定性。这些设备在有限的有向图上运行，充当相同的有限状态机的网络，这些无限状态机以无限次的同步回合序列进行通信。该问题在LogSpace中显示为可确定的对于一类健忘的自动机，节点会看到从邻居那里收到的消息，但不记得自己的状态。当限于适当的图族时，这些健忘的自动机等效于经典的有限词自动机，但是比有限树自动机具有更高的表达力。另一方面，我们还表明，空度问题通常是无法确定的。这已经适用于两类严格限制的分布式自动机：一类在每轮收到多条消息时立即拒绝，另一类状态图必须是非循环的，除了自循环。此外，为了展示分布式自动机在模拟不同计算模型时的灵活性，