Extension of parikh matrices to terms and its injectivity problem

Parikh matrices introduced by Mateescu et al. are very useful in understanding structural properties of words by analyzing their numerical properties. This is due to the information of a word provided by its Parikh matrix is more than its Parikh vector. The study of Parikh matrices is extended in this paper to terms formed over a signature with a binary underlying alphabet. We obtain some numerical properties that characterize when a word is a term. Finally, new M-equivalence preserving rewriting rules are introduced and shown to characterize M-equivalence for our terms, thus contributing towards the injectivity problem