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

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 $Π$ 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 $\cal C$.

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