Quotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languages

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.