Then, for a given path θ in A of size k: The last equation is because N (0) is the weight accumulated in all paths in the WFA, W A (Θ A (0, |Q| − 1, •)) (as we will see below), and W A (θ) is defined in a way similar to Equation (6).
the normalization keeps the relative weight distribution of the paths in the normalized PFA A .