Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages

摘要

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, and bifix-free regular languages. We prove that n~(n-2) is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix- and bifix-free regular languages, and conjecture tight upper bounds on their size.