Depth-two P systems can simulate Turing machines with NP oracles

• We consider the computing power of a model of polarizationless P systems with active membranes. • This model uses evolution, communication, dissolution, and (weak) membrane division rules. • We prove that these P systems compute at least all problems in the complexity class . • We do so by simulating nondeterministic Turing machines, used as oracles for a deterministic Turing machine. • The simulation is given for semi-uniform families of P systems, but it can be easily extended to uniform families. Among the computational features that determine the computing power of polarizationless P systems with active membranes, the depth of the membrane hierarchy is one of the least explored. It is known that this model of P systems can solve -complete problems when no constraints are given on the depth of the membrane hierarchy, whereas the complexity class P ∥ # P is characterized by monodirectional shallow P systems with minimal cooperation, whose depth is 1. No similar result is currently known for polarizationless systems without cooperation or other additional features. In this paper we show that these P systems, using a membrane hierarchy of depth 2, are able to solve at least all decision problems that are in the complexity class , the class of problems solved in polynomial time by deterministic Turing machines that are given the possibility to make a polynomial number of parallel queries to oracles for problems.