Appears in collection : Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme

The properties of finite dynamical systems have been investigated in the context of coding theoretic problems, such as network coding and index coding, and in the context of hat guessing games played on graphs. A causal network is an acyclic directed graph that represents the dependency of a collection of stochastic variables. The dependencies are assumed to be unknown, and one important question is to determine local rules that maximise the entropy of the system as a whole. We show that this problem is directly linked to fix-point problems in finite dynamical systems. Relying heavily on computer calculations we show that there is a deep link between fix points in finite dynamic systems, causal networks and information inequalities.