Matrix Insertion-Deletion Systems

TL;DR

This paper introduces matrix-controlled insertion and deletion systems, demonstrating that such systems with simple rules and binary matrices can achieve computational completeness, thus expanding the theoretical understanding of formal language systems.

Contribution

It is the first to analyze matrix-controlled insertion and deletion operations, showing their computational power with minimal rule complexity and binary matrices.

Findings

Matrix control increases computational power of insertion-deletion systems.

Systems with rules involving at most two symbols are computationally complete.

Binary matrices suffice to achieve computational completeness.

Abstract

In this article, we consider for the first time the operations of insertion and deletion working in a matrix controlled manner. We show that, similarly as in the case of context-free productions, the computational power is strictly increased when using a matrix control: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and using only binary matrices.