We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes by the existence and features of the fixed points of their corresponding automata. They are finite homogeneous paradoxes and infinite homogeneous paradoxes. In some weaker sense, we will also introduce no-no-sort paradoxes and virtual paradoxes. The introduction of these paradoxes, in turn, leads to a new classification of the cellular automata.

中文翻译：

---

基本细胞自动机和自我指称悖论

我们将基本的细胞自动机与一组自我指称的句子相关联，它们的修订过程正是该自动机的演变过程。这种连接的一个简单但有用的结果是，一组自指代句子是自相矛盾的，因为所讨论的细胞自动机没有固定点。我们通过其相应自动机的不动点的存在和特征来分类出几种不同的悖论。它们是有限齐次悖论和无限齐次悖论。从较弱的意义上讲，我们还将介绍“不排序”悖论和“虚拟悖论”。这些悖论的引入反过来导致了细胞自动机的新分类。