  The paper presents Entropy Semiring Forwardbackward algorithm (ESRFB) and its
application for memory efficient computation of the subsequence constrained
entropy and state sequence entropy of a Hidden Markov Model (HMM) when an
observation sequence is given. ESRFB is based on forward-backward recursion
over the entropy semiring, having the lower memory requirement than the
algorithm developed by Mann and MacCallum, with the same time complexity.
Furthermore, when it is used with forward pass only, it is applicable for the
computation of HMM entropy for a given observation sequence, with the same time
and memory complexity as the previously developed algorithm by Hernando et al
