Algebraic aspects of Parikh matrices

Abstract

This paper contains algebraic aspects of Parikh matrices. We present new, but also some old results, concerning this topic. It is proved that in some cases the set of Parikh matrices is a noncommutative semiring with a unit element. Also we prove that the set of Parikh matrices is closed under the operation of shuffle on trajectories and thus it is closed under many other operations. It is presented also the notion of extended Parikh matrix that it is an extension of the notion of the Parikh matrix. The paper contains also a number of open problems. © Springer-Verlag Berlin Heidelberg 2004.