# On the cyclic regularities of strings

## TL;DR

This paper introduces efficient algorithms for computing various cyclic regularities in strings, such as cyclic periodicity, all cyclic periodicity, maximal local cyclic periodicity, and cyclic covers, expanding the computational tools for string analysis.

## Contribution

The paper presents new algorithms specifically designed for computing cyclic regularities in strings, addressing gaps in existing methods for these particular properties.

## Key findings

- Algorithms for cyclic periodicity and all cyclic periodicity
- Algorithms for maximal local cyclic periodicity and cyclic covers
- Enhanced computational efficiency in string regularity analysis

## Abstract

Regularities in strings are often related to periods and covers, which have extensively been studied, and algorithms for their efficient computation have broad application. In this paper we concentrate on computing cyclic regularities of strings, in particular, we propose several efficient algorithms for computing: (i) cyclic periodicity; (ii) all cyclic periodicity; (iii) maximal local cyclic periodicity; (iv) cyclic covers.