A uniform solution to SAT using membrane creation

In living cells, new membranes are produced basically through two processes: mitosis and autopoiesis. These two processes have inspired two variants of cell-like membrane systems, namely P systems with active membranes and P systems with membrane creation. In this paper, we provide the first uniform, efficient solution to the SAT problem in the framework of recogniser P systems with membrane creation using dissolution rules. Recently the authors have proved that if the dissolution rules are not allowed to be used, then the polynomial complexity class associated with this variant of P systems is the standard complexity class P. This result, together with the main result of this paper, shows the surprising role of the apparently “innocent” operation of membrane dissolution. The use of this type of rule establishes the difference between efficiency and non-efficiency for P systems with membrane creation, and provides a barrier between P and NP (assuming P 6= NP). c © 2006 Elsevier B.V. All rights reserved.