Boolean networks are coarse-grained models of the regulatory dynamics for survival and proliferation of a living cell. The dynamics is time- and state-discrete. The Boolean abstraction assumes digital information processing. The binary distinction of a low or a high concentration of each bio-molecule is sufficient to capture the dynamics. In the presentation, I offer an introduction to Boolean networks, examples of application to specific biological systems and the mathematical and computational treatment with state transition graphs.
Despite being a drastic simplification w.r.t. systems of coupled differential equations, analysis of specific Boolean networks --- rather than ensemble averages --- poses computational challenges. I present ongoing work on capturing long term dynamics by identifying fixed points and other invariant sets under stochastic asynchronous update.