N-Insertion on Languages

Abstract

In this paper, we define the n-insertion A ⊳ [n] B of a language A into a language B and provide some properties of n-insertions. For instance, the n-insertion of a regular language into a regular language is regular but the n-insertion of a context-free language into a context-free language is not always context-free. However, it can be shown that the n-insertion of a regular (context-free) language into a context-free (regular) language is context-free. We also consider the decomposition of regular languages under n-insertion.