Computational Power of P Systems with Small Size Insertion and Deletion Rules

TL;DR

This paper demonstrates that integrating small-size insertion-deletion systems into P systems enhances their computational power, enabling them to generate all recursively enumerable languages, which they cannot do alone.

Contribution

The paper shows that P systems can elevate the computational power of small insertion-deletion systems to full Turing completeness.

Findings

Insertion-deletion systems alone are not computationally complete.

Embedding these systems in P systems achieves computational completeness.

The approach can generate any recursively enumerable language.

Abstract

Recent investigations show insertion-deletion systems of small size that are not complete and cannot generate all recursively enumerable languages. However, if additional computational distribution mechanisms like P systems are added, then the computational completeness is achieved in some cases. In this article we take two insertion-deletion systems that are not computationally complete, consider them in the framework of P systems and show that the computational power is strictly increased by proving that any recursively enumerable language can be generated. At the end some open problems are presented.