Various threshold Boolean networks (TBNs), a formalism used to model different types of biological networks (genes notably), can produce similar dynamics, i.e. share same behaviors. Among them, some are complex (according to Kolmogorov complexity), others not. By computing both structural and behavioral complexities, we show that most TBNs are structurally complex, even those having simple behaviors. For this purpose, we developed a new method to compute the structural complexity of a TBN based on estimates of the sizes of equivalence classes of the threshold Boolean functions composing the TBN.

中文翻译：

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关于计算阈值布尔网络的结构和行为复杂性

各种阈值布尔网络 (TBN)，一种用于模拟不同类型生物网络（特别是基因）的形式，可以产生类似的动态，即共享相同的行为。其中，有些是复杂的（根据 Kolmogorov 复杂性），有些则不是。通过计算结构和行为的复杂性，我们表明大多数 TBN 在结构上都很复杂，即使是那些具有简单行为的 TBN。为此，我们开发了一种新方法，基于对构成 TBN 的阈值布尔函数的等价类大小的估计，来计算 TBN 的结构复杂性。