Surface and curve languages

Abstract

In the area of combinatorial studies of string languages under formal grammars, the concept of Generalized Parikh Vector (GPV) gives the positions of symbols in linear strings. It has been proved that GPVs of the strings of the same length lie on a hyper plane. The studies on GPV of strings over a binary alphabet gave rise to the concept of line languages. The concept has been extended to surface languages in this paper.