Minimal cooperation as a way to achieve the efficiency in cell-like membrane systems

Cooperation is doubtless a relevant ingredient on rewriting rules based computing models. This paper provides an overview on both classical and newest results studying how cooperation among objects influences the ability of cell-like membrane systems to solve computationally hard problems in an efficient way. In this paper, two types of such membrane systems will be considered: (a) polarizationless P systems with active membranes without dissolution rules when minimal cooperation is permitted in object evolution rules; and (b) cell-like P systems with symport/antiport rules of minimal length. Specifically, assuming that P is not equal to NP, several frontiers of the efficiency are obtained in these two computing frameworks, in such manner that each borderline provides a tool to tackle the P versus NP problem.