  A language L is prefix-free if, whenever words u and v are in L and u is a
prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined
similarly, where "subword" means "subsequence". A language is bifix-free if it
is both prefix- and suffix-free. We study the quotient complexity, more
commonly known as state complexity, of operations in the classes of bifix-,
factor-, and subword-free regular languages. We find tight upper bounds on the
quotient complexity of intersection, union, difference, symmetric difference,
concatenation, star, and reversal in these three classes of languages.
