P systems with limited number of objects

P systems are a model of compartmentalized multiset rewriting inspired by the structure of living cells and the way they function. In this paper, we focus of a variant in P systems in which membranes have limited capacity, i.e., the number of objects they may hold is limited by a fixed bound. This feature corresponds to an important physical property of cellular compartments. We propose several possible semantics of limited capacity and show that one of them allows real-time simulations of partially blind register machines, while the other one allows for obtaining computational completeness.