On M-Equivalence and Strong M-Equivalence for Parikh Matrices

Abstract

The notion of strong [Formula: see text]-equivalence was introduced as an order-independent alternative to [Formula: see text]-equivalence for Parikh matrices. This paper further studies the notions of [Formula: see text]-equivalence and strong [Formula: see text]-equivalence. Certain structural properties of [Formula: see text]-equivalent ternary words are presented and then employed to (partially) characterize pairs of ternary words that are ME-equivalent (i.e. obtainable from one another by certain elementary transformations). Finally, a sound rewriting system in determining strong [Formula: see text]-equivalence is obtained for the ternary alphabet.