Malaysian Journal of Mathematical Sciences, April 2019, Vol. 13(S)
Special Issue: 3rd International Conference on Mathematical Sciences and Statistics (ICMSS2018)
Extension of Parikh Matrices to Terms and its Injectivity Problem
Chern, Z. J. and Teh, W. C.
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
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.
Keywords: Injectivity problem, \(M\)-equivalence, Parikh matrices, subword, terms
