Graph-Controlled Insertion-Deletion Systems

TL;DR

This paper explores graph-controlled insertion and deletion systems, demonstrating that their computational power significantly increases with a control graph of four nodes, even with rules involving at most two symbols.

Contribution

It introduces a novel framework combining graph control with insertion-deletion systems, establishing conditions for computational completeness with minimal rule size and control graph complexity.

Findings

Computational completeness achieved with at most two-symbol rules.

Control graph with four nodes suffices for full computational power.

Graph control enhances the capabilities of insertion-deletion systems.

Abstract

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: 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 with the control graph having only four nodes.