  A hidden Markov model (HMM) is said to have path-mergeable states if for any
two states i,j there exists a word w and state k such that it is possible to
transition from both i and j to k while emitting w. We show that for a finite
HMM with path-mergeable states the block estimates of the entropy rate converge
exponentially fast. We also show that the path-mergeability property is
asymptotically typical in the space of HMM topolgies and easily testable.
