Identities in twisted Brauer monoids

TL;DR

This paper proves that determining whether a semigroup identity holds in the twisted Brauer monoid is computationally hard (co-NP-hard) for n ≥ 5, highlighting complexity challenges in algebraic structures.

Contribution

It establishes the co-NP-hardness of identity verification in twisted Brauer monoids, a novel complexity result in algebraic semigroup theory.

Findings

Checking identities in twisted Brauer monoids is co-NP-hard for n ≥ 5.

Complexity results apply to algebraic structures with significant mathematical interest.

Abstract

We show that it is co-NP-hard to check whether a given semigroup identity holds in the twisted Brauer monoid $\mathcal{B}^\tau_n$ with $n\ge5$.