To perform belief update given a new visual input, we create a new wFSA to represent the likelihood of each character from the sample.
this wFSA has only a single chain of states, where, e.g., the first and second state in the chain are connected by 27 (or fewer) arcs, which emit each of the possible characters for w 1 along with their respective likelihoods given the visual input (as in the inner term of Equation 3).