2023/07/11 by Maximilien Gadouleau, Gadouleau, Maximilien, David C. Kutner +1
Computer Science · Biochemistry, Genetics and Molecular Biology · #Computational Drug Discovery Methods #Gene Regulatory Network Analysis #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2307.05216
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.