Abstract
The operations of symport and antiport, directly inspired frombiology, are already known to be rather powerful when used in the framework of P systems. In this paper we confirm this observation with a quite surprising result: P systems with symport/antiport rules using only three objects can simulate any counter machine, while systems with only two objects can simulate any blind counter machine. In the first case, the universality (of generating sets of numbers) is obtained also for a small number of membranes, four.