On Languages Generated by Context-Free Matrix Insertion-Deletion Systems with Exo-Operations

Matrix insertion-deletion systems are a class of insertion-deletion systems, where insertion and deletion rules are grouped in sequences, and it is known that such systems with two symbols context-free insertion and deletion rules are not computationally complete. In this work, matrix insertion-deletion systems with exo-operations (MIDEs, in short) are proposed, where insertion and deletion operations are applied only at the ends of a string (called exo-operations). The computation power of context-free MIDEs as language generators is investigated. We prove that context-free MIDEs of matrices size two with one symbol insertion and two symbols deletion are computationally complete, and so are systems with two symbols insertion and one symbol deletion. Moreover, if the size of matrices is three, the computational completeness can also be reached by context-free MIDEs with one symbol insertion and one symbol deletion. These results show that the computational power of MIDEs is strictly increased by introducing the exo-operations of insertion and deletion.

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