# Context-free word problem semigroups

## TL;DR

This paper explores classes of semigroups and monoids with context-free and deterministic context-free word problems, examining their properties, relationships, and closure under various algebraic constructions.

## Contribution

It provides new insights into the structure of these classes and their behavior under semigroup operations, linking them to word-hyperbolicity and automaticity.

## Key findings

- Examples illustrating class relationships
- Analysis of closure properties under semigroup constructions
- Connections with word-hyperbolicity and automaticity

## Abstract

This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the notions of word-hyperbolicity and automaticity. Second, a study is made of whether these classes are closed under applying certain semigroup constructions, including direct products and free products, or under regressing from the results of such constructions to the original semigroup(s) or monoid(s).