Universal Witnesses for State Complexity of Boolean Operations and Concatenation Combined with Star

TL;DR

This paper investigates the state complexity of boolean operations and concatenation involving starred languages, providing tight bounds and demonstrating that universal witnesses can meet these bounds.

Contribution

It introduces tight bounds for combined operations involving star and shows universal witnesses can meet these bounds, advancing understanding of language state complexity.

Findings

Derived tight upper bounds for boolean operations with starred languages

Universal witnesses can meet the bounds for various combined operations

Enhanced understanding of state complexity in regular language operations

Abstract

We study the state complexity of boolean operations and product (concatenation, catenation) combined with star. We derive tight upper bounds for the symmetric differences and differences of two languages, one or both of which are starred, and for the product of two starred languages. We prove that the previously discovered bounds for the union and the intersection of languages with one or two starred arguments, for the product of two languages one of which is starred, and for the star of the product of two languages can all be met by the recently introduced universal witnesses and their variants.