On the state complexity of closures and interiors of regular languages with subwords and superwords

TL;DR

This paper investigates the automata size and computational complexity of closures and interiors of regular languages formed by subwords and superwords, providing bounds and decision problem analyses.

Contribution

It introduces bounds on automata sizes for closures and interiors of regular languages and analyzes the complexity of related decision problems.

Findings

Bounds on automata size for closures and interiors

Complexity results for decision problems

Insights into the structure of regular language transformations

Abstract

The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all their subwords and superwords in $L$, respectively. We provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors. We also consider the computational complexity of decision problems for closures of regular languages.