On the number of useful objects in P systems with active membranes

TL;DR

This paper analyzes the number of objects actively used in specific polarizationless P systems with active membranes, demonstrating that their terminating computations can be bounded polynomially in object content per region.

Contribution

It establishes a polynomial upper bound on the objects in terminating computations of a particular class of P systems with active membranes, advancing understanding of their computational limits.

Findings

Polynomial bounds on object counts in terminating computations

Characterization of P systems without in-communication rules

Insights into the efficiency of polarizationless P systems

Abstract

In this paper we investigate the number of objects actually used in the terminating computations of a certain variant of polarizationless P systems with active membranes. The P systems we consider here have no in-communication rules and have no different rules triggered by the same object to manipulate the same membrane. We show that if we consider such a P system $\Pi$ and its terminating computation $\cal C$, then we can compute the result of $\cal C$ by setting a polynomial upper bound on the content of each region in $\cal C$.