Identities of triangular Boolean matrices

TL;DR

This paper characterizes the identities of upper triangular Boolean matrices, exploring their implications for computational complexity, axiomatization, and language recognition.

Contribution

It provides a combinatorial characterization of identities in the semiring of upper triangular Boolean matrices, linking algebraic properties to computational and language-theoretic aspects.

Findings

Identifies specific identities in the semiring of upper triangular Boolean matrices.

Connects algebraic identities to computational complexity of identity checking.

Offers insights into axiomatizability and language recognition related to these matrices.

Abstract

We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability of equational theories, and algebraic descriptions of certain classes of recognizable languages.