The longest-suffix prefix automaton for a finite set of forbidden factors

Let $\mathrm{\Sigma }$ be a finite alphabet and let $B$ be a finite nonempty set of nonempty words over $\mathrm{\Sigma }$. With $S_B$ as in Finite words, contiguous factors, avoidance and proper-prefix states, the prefix automaton for $B$ has state set $S_B$, initial state $\epsilon$, and the following transitions.

For $s\in S_B$ and $a\in \mathrm{\Sigma }$, reject the letter $a$ if the concatenation $sa$ contains a factor in $B$. Otherwise define $\delta (s,a)$ to be the longest suffix of $sa$ that belongs to $S_B$, and put an edge labelled $a$ from $s$ to $\delta (s,a)$. This state exists because $\epsilon \in S_B$, and it is unique because suffixes of distinct lengths are distinct.

For enumeration, give every edge weight $1$ over $\mathbb{Z}$. Different letters that induce the same transition remain parallel edges, so the associated transfer-matrix entry is the number of such letters.