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

TL;DR

This paper investigates the state complexity of various operations on bifix-, factor-, and subword-free regular languages, establishing tight bounds for their quotient complexity.

Contribution

It provides the first comprehensive analysis of the quotient complexity bounds for multiple operations within these specific classes of regular languages.

Findings

Tight upper bounds for intersection, union, difference, symmetric difference, concatenation, star, and reversal.

Exact quotient complexity bounds for bifix-, factor-, and subword-free languages.

Enhanced understanding of the computational complexity of these language classes.

Abstract

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.