State Complexity Investigations on Commutative Languages -- The Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages

TL;DR

This paper explores the state complexity of various closure and shuffle operations on commutative regular, group, and aperiodic languages, providing systematic analysis and new insights into their computational properties.

Contribution

It offers a systematic study of the state complexity of closure, interior, and shuffle operations on commutative languages, including group and aperiodic languages, filling gaps in existing research.

Findings

Detailed state complexity bounds for closure and interior operations

Analysis of shuffle operation complexity on commutative languages

Insights into the computational properties of commutative group and aperiodic languages

Abstract

We investigate the state complexity of the upward and downward closure and interior operations on commutative regular languages. Then, we systematically study the state complexity of these operations and of the shuffle operation on commutative group languages and commutative aperiodic (or star-free) languages.