By unique words we understand the such word $w$ that every character in the word occur at most once, for example:$\Sigma = \{a,b,c\}$$w = abc$, $v = abca$$w$ is unique, $v$ is not.Now, we have a problem:We have given an alphabet $\Sigma$. We have a given length of word $|w| = n$. How to recognize using $NFA$ whether $w$ is unique?$NFA$ is expected to has polynomial number of states regard to $n$.Please hint me.
A recognizing unique words
complexity theory;finite automata;nondeterminism