Let's recall the WFSA B (Figure 1 and Example 5) using the real semiring hR, +, •, 0, 1i.
equation 6 is recovered by parameterizing B's weight functions µ and with Denote the resulting WFSA by B i , and we have: Running a single layer RNN in example 6 over any nonempty input string x 2 ⌃ + , the ith dimension of its hidden state at time step t equals the score assigned by B i to x :t : the ith dimension of the RNN in example 6 can be seen as a WFSA structurally equivalent to B.