  Minimal forbidden factors are a useful tool for investigating properties of
words and languages. Two factorial languages are distinct if and only if they
have different (antifactorial) sets of minimal forbidden factors. There exist
algorithms for computing the minimal forbidden factors of a word, as well as of
a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an
algorithm that, given the trie recognizing a finite antifactorial language $M$,
computes a DFA recognizing the language whose set of minimal forbidden factors
is $M$. In the same paper, they showed that the obtained DFA is minimal if the
input trie recognizes the minimal forbidden factors of a single word. We
generalize this result to the case of a circular word. We discuss several
combinatorial properties of the minimal forbidden factors of a circular word.
As a byproduct, we obtain a formal definition of the factor automaton of a
circular word. Finally, we investigate the case of minimal forbidden factors of
the circular Fibonacci words.
