On M-Equivalence And Strong M-Equivalence For Parikh Matrices

The notion of strong M-equivalence was introduced as an order-independent alternative to M-equivalence for Parikh matrices. This paper further studies the notions of M-equivalence and strong M-equivalence. Certain structural properties of M-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 M-equivalence is obtained for the ternary alphabet.