Algebraic Properties of Boolean Models

Boolean models are n-tuples of polynomial functions in n variables over the finite field of order 2. These models define finite dynamical systems which are used for modeling many different biological systems such as gene regulatory networks. These systems can be defined by updating every function synchronously, or by updating one function at a time asynchronously. In this project, we discuss a method for reverse engineering the model space of all Boolean models which fit a set of partial asynchronous data. This method is a generalization of a known method for synchronous data. In addition, we show that given the interaction graph, or wiring diagram, of a composition of two Boolean functions h = f ◦ g, we can infer characteristics of the wiring diagrams of f and g. This is an initial step to studying how the wiring diagrams change under topological conjugation, which is a problem that has recently been proposed.