k-Local Internal Contextual Grammars

In this paper we propose a generalization of the local internal contextual grammars, introduced by Ilie in 1997, namely the k-local internal contextual grammars. These grammars are, in fact, classical internal contextual grammars, but their only permitted derivations are those that can be described in a restricted manner (that depends on the number k). Within this formalism we define different classes of languages, for which we prove a series generative properties. Also, we propose an efficient algorithmic solution for the membership problem for k-local contextual grammars with polynomial choice. This seems interesting to us, as it shows how the restrictions on the descriptions of the derivations reflect in the possibility of designing a polynomial algorithm for the acceptance of the languages generated by internal contextual grammars using such derivations.