  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.
