We consider the asynchronous prediction problem for some automaton as the one consisting in determining, given an initial configuration, if there exists a non-zero probability that some selected site changes its state, when the network is updated picking one site at a time uniformly at random.

We show that for the majority automaton, the asynchronous prediction problem is in NC in the two-dimensional lattice with von Neumann neighborhood. Later, we show that in three or more dimensions the problem is NP-Complete.

中文翻译：

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多数自动机异步预测的复杂性

我们将某些自动机的异步预测问题视为一种自动确定异步机的问题，即在给定初始配置的情况下，当网络一次均匀地选择一个站点进行更新时，确定某个选定站点是否存在非零概率改变其状态。随机。

我们表明，对于多数自动机，异步预测问题是在具有冯·诺依曼邻域的二维晶格中的NC中进行的。后来，我们证明了在三个或更多个维度中问题是NP -Complete。