# On avoidability of formulas with reversal

## TL;DR

This paper investigates the avoidability of formulas with reversal, providing a characterization of unavoidable formulas with at most two one-way variables, extending known results from formulas without reversal.

## Contribution

It offers the first characterization of unavoidable formulas with reversal involving up to two one-way variables, advancing the understanding of avoidability in this context.

## Key findings

- Characterization of unavoidable formulas with reversal and at most two one-way variables
- Extension of avoidability theory to formulas with reversal
- Provides foundational results for future research in combinatorics on words

## Abstract

While a characterization of unavoidable formulas (without reversal) is well-known, little is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas with reversal that have at most two one-way variables ($x$ is a one-way variable in formula with reversal $\phi$ if exactly one of $x$ and $x^R$ appears in $\phi$).