The non-abelian squares are not context-free

TL;DR

This paper proves that the set of words that are not abelian squares cannot be described by a context-free grammar, answering a recent open question in formal language theory.

Contribution

It establishes that the language of non-abelian squares is not context-free, resolving a recent open problem in the field.

Findings

The language of non-abelian squares is not context-free.

Provides a formal proof resolving an open question.

Advances understanding of language classes in formal language theory.

Abstract

Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free.