The asynchronous automaton associated with a Boolean network $f:{\{0,1\}}^n\to {\{0,1\}}^n$ is considered in many applications. It is the finite deterministic automaton with set of states ${\{0,1\}}^n$, alphabet $\{1,\dots ,n\}$, where the action of letter i on a state x consists in switching the ith component if $f_i(x)\ne x_i$ or doing nothing otherwise. This action is extended to words in the natural way. We then say that a word w fixes f if, for all states x, the result of the action of w on x is a fixed point of f. In this paper, we ask for the existence of fixing words, and their minimal length. Firstly, our main results concern the minimal length of words that fix monotone networks. We prove that there exists a monotone network f with n components such that any word fixing f has length $\mathrm{\Omega }(n^2)$. Conversely, we construct a word of length $O(n^3)$ that fixes all monotone networks with n components. Secondly, we refine and extend our results to different classes of networks.

与布尔网络关联的异步自动机 $F：{\{0，\mathrm{1个}\}}^{ñ}\to {\{0，\mathrm{1个}\}}^{ñ}$被认为在许多应用中。它是带有状态集的有限确定性自动机${\{0，\mathrm{1个}\}}^{ñ}$， 字母 $\{\mathrm{1个}，\dots ，ñ\}$，其中字母的作用我上的状态X在于切换我如果个分量$F_{\mathrm{一世}}（X）\ne X_{\mathrm{一世}}$或不做任何其他事情。此动作以自然方式扩展到单词。然后我们说，如果对于所有状态x，w对x的作用的结果是f的固定点，则单词w固定f。在本文中，我们要求固定词的存在及其最小长度。首先，我们的主要结果涉及固定单调网络的单词的最小长度。我们证明存在一个具有n个成分的单调网络f，使得任何固定词f的长度$\mathrm{\Omega }（{ñ}^2）$。相反，我们构造一个长度词$Ø（{ñ}^3）$修复具有n个分量的所有单调网络。其次，我们将结果优化并扩展到不同类别的网络。