Context-free insertion–deletion systems

Abstract

We consider a class of insertion–deletion systems which have not been investigated so far, those without any context controlling the insertion–deletion operations. Rather unexpectedly, we found that context-free insertion–deletion systems characterize the recursively enumerable languages. Moreover, this assertion is valid for systems with only one axiom, and also using inserted and deleted strings of a small length. As direct consequences of the main result we found that set-conditional insertion–deletion systems with two axioms generate any recursively enumerable language (this solves an open problem), as well as that membrane systems with one membrane having context-free insertion–deletion rules without conditional use of them generate all recursively enumerable languages (this improves an earlier result). Some open problems are also formulated.