k-Local Internal Contextual Grammars
- Cite this paper as:
- Gramatovici R., Manea F. (2011) k-Local Internal Contextual Grammars. In: Holzer M., Kutrib M., Pighizzini G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg
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). Using this formalism we define different classes of languages, and obtain a series of language theoretic results for them. Also, we show that the membership problem for k-local internal contextual grammars with polynomial choice can be solved in polynomial time. This seems interesting to us, as it shows that the descriptional restrictions on the derivations of a grammar reflect on the computational efficiency of accepting the language generated by that grammar.
KeywordsInternal contextual grammars k-Local Derivation Hierarchy of languages Membership problem
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