A Polynomial-Time Criterion for Stability in Distribution of Probabilistic Boolean Networks

This paper studies the stability in distribution of large-scale probabilistic Boolean networks (PBNs) from the graph-theoretic aspect. The node removal technique is firstly developed to find the fixed points with probability one of PBNs. Then, combining Thomas' rule in Boolean case and node removal technique, a polynomial-time criterion is established for the stability in distribution of PBNs when there exists a mode whose network graph is acyclic. The effectiveness of the criterion is illustrated by the PBN model of Pancreatic Cancer network.