In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each time-step only one cell is updated. We define the problem AsyncUnstability, which consists in deciding there exists a sequential updating scheme that changes the state of a given cell.

We begin showing that AsyncUnstability is in NL for any one-dimensional FCA. Then we focus on the family of life-like freezing CA (LFCA). We study the complexity of AsyncUnstability for all LFCA in the triangular and square grids, showing that almost all of them can be solved in NC, except for one rule for which the problem is NP-Complete.

在本文中，我们在异步更新方案的背景下研究了冻结元胞自动机 (FCA) 系列。如果元胞自动机的状态存在顺序，则该元胞自动机称为冻结，并且仅允许从较低状态到较高状态进行转换。如果在每个时间步仅更新一个单元格，则元胞自动机是异步的。我们定义了问题AsyncUnstability，它包括确定存在一个改变给定单元状态的顺序更新方案。

我们开始证明对于任何一维FCA ，AsyncUnstability在NL中。然后我们重点介绍一下栩栩如生的冷冻CA（LFCA）家族。我们研究了三角形和方形网格中所有 LFCA的AsyncUnstability的复杂性，表明几乎所有这些都可以在NC 中解决，除了一个问题是NP -Complete 的规则。