  Given a language L and a nondeterministic finite automaton M, we consider
whether we can determine efficiently (in the size of M) if M accepts at least
one word in L, or infinitely many words. Given that M accepts at least one word
in L, we consider how long a shortest word can be. The languages L that we
examine include the palindromes, the non-palindromes, the k-powers, the
non-k-powers, the powers, the non-powers (also called primitive words), the
words matching a general pattern, the bordered words, and the unbordered words.
