State complexity of orthogonal catenation

TL;DR

This paper establishes a precise and tight bound on the state complexity of orthogonal catenation of regular languages, showing it is smaller than the bound for general catenation, thus advancing understanding of language operations.

Contribution

It provides the first tight bound for the state complexity of orthogonal catenation, a specific language operation, highlighting differences from general catenation.

Findings

The bound for orthogonal catenation is strictly smaller than for arbitrary catenation.

The paper proves the tightness of the bound.

It advances theoretical understanding of language operation complexities.

Abstract

A language $L$ is the orthogonal catenation of languages $L_1$ and $L_2$ if every word of $L$ can be written in a unique way as a catenation of a word in $L_1$ and a word in $L_2$. We establish a tight bound for the state complexity of orthogonal catenation of regular languages. The bound is smaller than the bound for arbitrary catenation.