A dozen of research topics in membrane computing.

This note considers three basic research directions in membrane computing – characterizations of the computing power of Turing machines, computing more than Turing machines, efficiency (solving computationally hard problems in a feasible time) – by basic classes of P systems (cell and tissue multiset rewriting systems, symport/antiport systems, spiking neural P systems, numerical P systems). (Types of) Results reported in the literature are briefly mentioned, several unsolved cases are pointed out, and directions of further research are proposed.