Subregular Expressions and Their Expressive Power

Abstract

We provide a survey of several families of subregular expressions obtained by modifying the classical operator set consisting of union, concatenation, and Kleene star. More specifically, we consider expression systems based on sets of two or three operations chosen from union, intersection, complementation, concatenation, and Kleene star. The resulting language families range from finite languages to the full class of regular languages. We collect and organize known results on the expressive power and structural properties of these families. We compare the resulting language classes over unary and arbitrary alphabets and summarize known inclusion, equality, and incomparability results. The aim of this survey is to provide a unified view of the language families induced by restricted operator sets and to highlight open relations and possible directions for further research.