Depth-two P systems can simulate Turing machines with NP oracles - Leporati, Alberto; Manzoni, Luca; Mauri, Giancarlo; Zandron, Claudio (Theoretical computer science, 2022)
•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.