State complexity of union and intersection combined with star and reversal

TL;DR

This paper investigates the state complexities of combined operations involving union, intersection, star, and reversal on regular languages, revealing they are less complex than the composition of individual operation complexities.

Contribution

It provides new bounds on state complexities for combined operations, showing they are lower than expected from simple composition.

Findings

State complexities of combined operations are less than the product of individual complexities.

Derived explicit formulas for the state complexities of combined union and intersection with star and reversal.

Results improve understanding of automata state requirements for complex regular language operations.

Abstract

In this paper, we study the state complexities of union and intersection combined with star and reversal, respectively. We obtain the state complexities of these combined operations on regular languages and show that they are less than the mathematical composition of the state complexities of their individual participating operations.