In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors.

We classify all the Cellular Automata in the class of TFCA, grouping them in five different classes: the Trivial rules, Turing Universal rules, Algebraic rules, Topological rules and Fractal Growing rules. At the same time, we study in this family the Stability problem, consisting in deciding whether an inactive cell becomes active, given an initial configuration. We exploit the properties of the automata in each group to show that:

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For Algebraic and Topological Rules the Stability problem is in NC.

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For Turing Universal rules the Stability problem is P-Complete.

在本文中，我们研究了在具有冯·诺伊曼（von Neumann）邻域的三角形和正方形网格上定义的二态全能冻结细胞自动机（TFCA）族。我们说，如果活动单元格保持不变，则元胞自动机将处于冻结状态并处于总体状态，并且非活动单元格的新值仅取决于其活动邻居的总和。

我们将所有细胞自动机分类为TFCA类，将它们分为五个不同的类：琐碎的规则，图灵通用规则，代数规则，拓扑规则和分形增长规则。同时，我们在这个家族中研究稳定性问题，包括在给定初始配置的情况下确定不活动的电池是否变为活动状态。我们利用每个组中自动机的属性来显示：

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对于代数和拓扑规则，稳定性问题在NC中。

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对于图灵通用规则，稳定性问题为P-完全。