The freeness problem over matrix semigroups and bounded languages

TL;DR

This paper investigates the decidability of the freeness problem in matrix semigroups, demonstrating that it is decidable for upper-triangular 2x2 rational matrices under certain bounded language restrictions.

Contribution

It establishes the decidability of the freeness problem for a specific class of matrix semigroups with bounded language constraints, extending previous understanding.

Findings

Freeness problem is decidable for upper-triangular 2x2 rational matrices.

Decidability holds when products are restricted to certain bounded languages.

Provides new insights into matrix semigroup properties under language restrictions.

Abstract

We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular $2\times 2$ matrices with rational entries when the products are restricted to certain bounded languages.