Computing by Communication in Networks of Membranes

In this paper we consider networks of membranes which compute by communication only, using symport/antiport rules. Such rules are used both for communication with the environment and for direct communication among membranes. It turns out that, rather surprisingly, networks with a small number of membranes are computationally universal. This is proved both for the case of three membranes where each membrane communicates with each other membrane, and for the case of four membranes consisting of two pairs such that only the membranes within each pair communicate directly. A single pair of communicating membranes can compute the Parikh images of matrix languages. Several open problems are also formulated.