The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its neighbourhood. In general, the convergence of the so-called kernel network is complex. A word (sequence of vertices) fixes the kernel network if applying the updates sequentially according to that word. We prove that determining whether a word fixes the kernel network is coNP-complete. We also consider the so-called permis, which are permutation words that fix the kernel network. We exhibit large classes of graphs that have a permis, but we also construct many graphs without a permis.

翻译：寻找图的最大独立集的简单贪心算法可被视为布尔网络的顺序更新过程，其中每个顶点的更新函数是其邻域内所有否定变量的合取。一般而言，所谓核网络的收敛性具有复杂性。若按某个单词（顶点序列）顺序执行更新操作可使该网络固定，则称该单词固定了核网络。我们证明判定一个单词是否固定核网络是coNP完全的。同时我们研究了所谓的"permis"（即能固定核网络的置换单词），并发现了若干具有permis的图类，但也构造了大量不含permis的图。