P AUTOMATA WITH RESTRICTED POWER

P automata are variants of symport/antiport membrane systems which describe string languages by applying a mapping to the sequence of multisets entering the system during computations. In this paper, we study their computational power in the case when the input mapping associates each input multiset with the set of strings consisting of all permutations of its elements. We show that P automata of this type are strictly less powerful than so-called restricted logarithmic space Turing machines, and we also exhibit a strict infinite hierarchy within the accepted language class based on the number of membranes present in the system.