Universal Matrix Insertion Grammars with Small Size

Abstract

We study matrix insertion grammars (MIS) towards representation of recursively enumerable languages with small size. We show that pure MIS of size (3; 1, 2, 2) (i.e., having ternary matrices inserting one symbol in two symbol context) can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language or an intersection with a regular language followed by a weak coding. The obtained results complete known results on insertion-deletion systems from DNA computing area.