Generative Power of Matrix Insertion-Deletion Systems with Context-Free Insertion or Deletion

Abstract

Matrix insertion-deletion systems combine the idea of matrix control as established in regulated rewriting with that of insertion and deletion as opposed to replacements. We improve on and complement previous computational completeness results for such systems, showing for instance that matrix insertion-deletion systems with matrices of length two, insertion rules of type 1,i?ź1,i?ź1 and context-free deletions are computationally complete. We also show how to simulate Kleene stars of metalinear languages with several types of systems with very limited resources. We also generate non-semilinear languages using matrices of length three with context-free insertion and deletion rules.