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

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 $\mathcal{C}$, then we can compute the result of $\mathcal{C}$ by setting a polynomial upper bound on the content of each region in $\mathcal{C}$.