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 eight states and six-letter alphabets.
