Epsilon-machines are minimal, unifilar presentations of stationary stochastic
processes. They were originally defined in the history machine sense, as hidden Markov
models whose states are the equivalence classes of infinite pasts with the same probability
distribution over futures. In analyzing synchronization, though, an alternative generator
definition was given: unifilar, edge-emitting hidden Markov models with probabilistically
distinct states. The key difference is that history epsilon-machines are defined by a
process, whereas generator epsilon-machines define a process. We show here that these two
definitions are equivalent in the finite-state case
