Identities of triangular Boolean matrices
Group Theory
2025-10-08 v4 Combinatorics
Abstract
We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean -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.
Cite
@article{arxiv.2412.16113,
title = {Identities of triangular Boolean matrices},
author = {Mikhail V. Volkov},
journal= {arXiv preprint arXiv:2412.16113},
year = {2025}
}
Comments
23 pages. In version 3, the proof of the main result is reorganized, two new corollaries are added, and Propositions 3.3 and 3.9 are provided with detailed proofs. In version 4, Example 2.4 is added