Symbolic dynamics of Boolean control networks

We consider Boolean control networks (BCNs), and in particular Boolean networks (BNs), in the framework of symbolic dynamics (SD). We show that the set of state-space trajectories of a BCN is a shift space of finite type (SFT). This observation allows us to extend two important analysis tools from SD, namely, the Artin–Mazur zeta function and the topological entropy, to BNs and BCNs. Some of the theoretical results are illustrated using a BCN model of the core network regulating the mammalian cell cycle.