Asynchronous and Maximally Parallel Deterministic Controlled Non-Cooperative P Systems Characterize NFIN coNFIN

Membrane systems (with symbol objects) are distributed controlled multiset processing systems. Non-cooperative P systems with either promoters or inhibitors (of weight not restricted to one) are known to be computationally complete. In this paper we show that the power of the deterministic subclass of such systems is computationally complete in the sequential mode, but only subregular in the asynchronous mode and in the maximally parallel mode.