This paper investigates the monostability and bistability of Boolean networks using semitensor products (STPs). A theorem characterizing the stability of a Boolean network is presented and then used to develop three new algorithms. The first determines the stability in $O(2^n)$, a marked improvement of the complexity of $O((2^n-1)2^{2.81n})$, the results from simply using Strassen's recursive algorithm. The second algorithm computes the transient period of a given system state, and the last one maximizes this over an entire Boolean network. We conclude by applying these algorithms to two published Boolean models of well-known biological networks in E. coli.

中文翻译：

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使用半张量积的布尔网络的单稳定性和双稳态

本文研究使用半张量积（STP）的布尔网络的单稳定性和双稳态。提出了表征布尔网络稳定性的定理，然后将其用于开发三种新算法。首先确定稳定性$ O（2 ^ n）$，显着改善了 $ O（（2 ^ n-1）2 ^ {2.81n}）$，只需使用Strassen的递归算法即可得出结果。第二种算法计算给定系统状态的瞬态周期，最后一种算法在整个布尔网络上将其最大化。我们通过将这些算法应用到两个已发布的知名生物网络的布尔模型中得出结论大肠杆菌。