Abstract
Membrane systems (P systems) are computational models of processes which take place in living cells. Here we investigate the power of the original version of P systems introduced in Păun (1998), called simple P systems in Păun (2002). On one hand, we show that P systems with catalysts, without any other additional feature, are computationally universal. This rather surprising result improves some previous universality theorems of P systems, including the fundamental ``computational completeness lemma for P systems'' Păun (1998), and solves the open problem Q1 in Păun (2002). On the other hand, we show that the power of P systems with priorities but without interactions (open problem Q2) does not exceed the power of ET0L systems with random context regulation without appearance checking.
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