Permutations of context-free and indexed languages

TL;DR

This paper investigates how certain language operations, specifically cyclic closure and the operators $C^k$, affect the classification of languages within formal language theory, showing that these operations preserve or produce indexed languages.

Contribution

It proves that the cyclic closure of an indexed language remains indexed, and that applying the $C^k$ operator to a context-free language results in an indexed language.

Findings

Cyclic closure of an indexed language is indexed.

Applying $C^k$ to a context-free language yields an indexed language.

The results extend understanding of language operations in formal language hierarchy.

Abstract

We consider the cyclic closure of a language, and its generalisation to the operators $C^k$ introduced by Brandst\"adt. We prove that the cyclic closure of an indexed language is indexed, and that if $L$ is a context-free language then $C^k(L)$ is indexed.