Free inverse monoids are co-context-free

TL;DR

This paper proves that the co-word problem of free inverse monoids of any finite rank is context-free, using grammatical methods, which advances understanding of their formal language properties.

Contribution

It establishes that free inverse monoids of finite rank have co-context-free word problems, a novel result in algebraic language theory.

Findings

The co-word problem of free inverse monoids is context-free.

The proof uses grammatical methods to establish the property.

This result applies to all finite ranks of free inverse monoids.

Abstract

We prove (using grammars) that the free inverse monoid of every finite rank has co-context-free word problem. Equivalently, the co-word problem of the free inverse monoid of every finite rank is context-free.