On generalized communicating P systems with minimal interaction rules

Generalized communicating P systems are purely communicating tissue-like membrane systems with communication rules which allow the movement of only pairs of objects. In this paper, we study the power of these systems in the case of eight restricted variants of communication rules. We show that seven of these restrictions lead to computational completeness, while using the remaining one the systems are able to compute only finite singletons of non-negative integers. The obtained results complete the investigations of the computational power of generalized communicating P systems and provide further examples for simple architectures with simple functioning rules which are as powerful as Turing machines.