State complexity of catenation combined with a boolean operation: a unified approach

TL;DR

This paper investigates the state complexity of combining catenation with boolean operations, providing tight bounds and a unified method applicable to various combinations, including union, intersection, and symmetric difference.

Contribution

It introduces a unified approach to determine the state complexity of catenation combined with any binary boolean operation, extending previous specific studies.

Findings

Upper bounds for state complexity are computed using combinatoric tools.

The bounds are shown to be tight with explicit witnesses.

A unified method applies to multiple boolean operations with catenation.

Abstract

In this paper we study the state complexity of catenation combined with symmetric difference. First, an upper bound is computed using some combinatoric tools. Then, this bound is shown to be tight by giving a witness for it. Moreover, we relate this work with the study of state complexity for two other combinations: catenation with union and catenation with intersection. And we extract a unified approach which allows to obtain the state complexity of any combination involving catenation and a binary boolean operation.