On the Number of Membranes in Unary P Systems

TL;DR

This paper investigates unary P systems with linear membrane structures, showing they have unique minimal representations and an effective equivalence problem solution, while analyzing their descriptional complexity.

Contribution

It introduces a restricted unary P system model with unique minimal representations and studies their complexity relative to the number of membranes.

Findings

Unique minimal representation for unary P systems

Effective solution for the equivalence problem

Analysis of descriptional complexity based on membrane count

Abstract

We consider P systems with a linear membrane structure working on objects over a unary alphabet using sets of rules resembling homomorphisms. Such a restricted variant of P systems allows for a unique minimal representation of the generated unary language and in that way for an effective solution of the equivalence problem. Moreover, we examine the descriptional complexity of unary P systems with respect to the number of membranes.