Problem 60: Minimal Absent Words
Words that do not occur in files provide a useful technique to discard or
discriminate files.
They act like the set of factors of a file but admit a
more compact trie representation as factor codes.
A word $w$, $|w|\gt 1$, is said to be absent or forbidden in a word $x$ if it
does not occur in $x$.
It is said to be minimal with this property if in
addition both $w[0\dd |w|-2]$ and $w[1\dd |w|-1]$ do occur in $x$.
A natural method to compute the minimal words absent in $x$ is to start with
its Factor automaton $\aFact(x)$, smallest deterministic automaton accepting
all its factors.
Each factor is spelt out along a path starting from the
initial state and all states are terminal.
Design a linear-time algorithm to compute the trie of minimal absent words of
a word $x$ from its Factor automaton $\aFact(x)$.
Use failure links of the automaton.
Design a linear-time algorithm to recover the Factor automaton of a word $x$
from the trie of its minimal absent words.
Use the Aho-Corasick technique.
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