Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a regulatory (local) function specifying its dynamical behaviour depending on its regulators. However, existing data is mostly insufficient to adequately parametrise a model, that is to uniquely define a regulatory function for each node. With the intend to support model parametrisation, this paper presents results on the set of Boolean functions compatible with a given regulatory structure, i.e. the partially ordered set of monotone non-degenerate Boolean functions. More precisely, we present original rules to obtain the direct neighbours of any function of this set. Besides a theoretical interest, presented results will enable the development of more efficient methods for Boolean network synthesis and revision, benefiting from the progressive exploration of the vicinity of regulatory functions.

翻译：布尔网络是研究遗传与信号网络行为的重要数学模型。这些网络定义了分子节点间的调控影响，每个节点关联一个布尔变量及一个调控（局部）函数，该函数根据其调控因子指定其动态行为。然而，现有数据大多不足以充分参数化模型，即无法为每个节点唯一定义调控函数。为支持模型参数化，本文针对与给定调控结构兼容的布尔函数集合——即单调非退化布尔函数的偏序集——提出了若干研究结果。具体而言，我们提出了获取该集合中任意函数直接邻域的原创新规则。除理论价值外，所提结果将有助于开发更高效的布尔网络合成与修正方法，其优势在于能够逐步探索调控函数邻域。