Freeness Problem for Matrix Semigroups of Parikh Matrices

Abstract

Since the undecidability of the mortality problem for 3 × 3 matrices over integers was proved using the Post Correspondence Problem, various studies on decision problems of matrix semigroups have emerged. The freeness problem in particular has received much attention but decidability remains open even for 2 × 2 upper triangular matrices over nonnegative integers. Parikh matrices are upper triangular matrices introduced as a generalization of Parikh vectors and have become useful tools in studying of subword occurrences. In this work, we focus on semigroups of Parikh matrices and study the freeness problem in this context.