Given a function f: Bⁿ → Bⁿ where B = {0,1}, we construct two digraphs. The first, called the State Transition Graph (STG), describes a discrete dynamical system on Bⁿ derived from f. The second, called the Interaction Graph (IG), graphically represents the influence of each input on each output of f. In the IG, an activating influence is a positive edge and an inhibiting influence is negative. These graphs form the foundation of a discrete model of gene regulatory networks. I will present proofs of two conjectures of René Thomas in this framework, the first that a positive cycle in the IG is a necessary condition for the presence of multiple fixed points in the STG and the second that a negative cycle in the IG is a necessary condition for the presence of an attractive cycle in the STG.