We revisit the problem of deciding whether a given string is uniquely
decodable from its bigram counts by means of a finite automaton. An efficient
algorithm for constructing a polynomial-size nondeterministic finite automaton
that decides unique decodability is given. Conversely, we show that the minimum
deterministic finite automaton for deciding unique decodability has at least
exponentially many states in alphabet size.Comment: 12 page