Enumerating Finitary Processes

We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of ε-machines. We characterize ε-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large class down to that of ε-machines. As an application, we exactly enumerate topological ε-machines up to seven states and six-letter alphabets.