On P Systems with Active Membranes

The paper deals with the vivid area of computing with membranes (P systems). We improve here two recent results about the socalled P systems with active membranes. First, we show that the Hamiltonian Path Problem can be solved in polynomial time by P systems with active membranes where the membranes are only divided into two new membranes (a result of this type was obtained by Krishna and Rama, [4], but making use of the possibility of dividing a membrane in an arbitrary number of new membranes). We also show that HPP can be solved in polynomial time also by a variant of P systems, with the possibility of dividing non-elementary membranes under the influence of objects present in them. Then, we show that membrane division (and even membrane dissolving) is not necessary in order to show that such systems are computationally complete.