One-dimensional Array Grammars and P Systems with Array Insertion and Deletion Rules

TL;DR

This paper explores the computational power of one-dimensional array grammars and P systems with array insertion and deletion rules, establishing undecidability results and demonstrating their computational completeness with rules of limited norm.

Contribution

It introduces the computational capabilities of array insertion and deletion rules in one-dimensional array grammars and P systems, showing their completeness with rules of norm at most two.

Findings

Undecidability of the emptiness problem for P systems with insertion rules.

Computational completeness of P systems with array insertion and deletion rules of norm one.

Computational completeness of one-dimensional array grammars with rules of norm at most two.

Abstract

We consider the (one-dimensional) array counterpart of contextual as well as insertion and deletion string grammars and consider the operations of array insertion and deletion in array grammars. First we show that the emptiness problem for P systems with (one-dimensional) insertion rules is undecidable. Then we show computational completeness of P systems using (one-dimensional) array insertion and deletion rules even of norm one only. The main result of the paper exhibits computational completeness of one-dimensional array grammars using array insertion and deletion rules of norm at most two.