On Rystov's generalization of the \v{C}ern\'y Conjecture

TL;DR

This paper resolves Rystov's conjecture, which generalizes the cerny Conjecture, by analyzing matrix products and providing new insights into automata theory and matrix behavior.

Contribution

It proves Rystov's conjecture, extending the cerny Conjecture to a broader class of matrix products, a novel theoretical advancement.

Findings

Confirmed Rystov's conjecture for matrix products

Extended cerny Conjecture to matrices

Provided new theoretical framework for matrix automata

Abstract

We resolve a conjecture of Rystov concerning products of matrices, that generalizes the \v{C}ern\'y Conjecture.