# Inverse monoids associated with the complexity class NP

## TL;DR

This paper explores the P versus NP problem by examining inverse monoids and their properties, aiming to understand the existence of one-way functions and the fundamental complexity class distinctions.

## Contribution

It introduces a novel algebraic approach using inverse monoids to analyze P vs NP and the existence of injective one-way functions.

## Key findings

- Inverse monoid properties relate to P vs NP status
- Characterization of one-way functions through monoid structures
- Provides algebraic criteria for complexity class separation

## Abstract

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective one-way functions (with respect to worst-case complexity) exist.