An Asynchronous P System Using Branch and Bound for the Satisfiability Problem

Membrane computing, which is a computational model based on cell activity, has considerable attention as one of new paradigms of computations. In the general membrane computing, computationally hard problems have been solved in a polynomial number of steps using an exponential number of membranes. However, reduction of the number of membranes must be considered to make P system more realistic model. In the paper, we propose an asynchronous P system using branch and bound, which is a well known optimization technique, to reduce the number of membranes. The proposed P system solves the satisfiability problem (SAT) with n variables and m clauses, and works in O(m2ⁿ) sequential steps or O(mn) parallel steps. The number of membranes used in the proposed P system is evaluated using a computational simulation. The experimental result shows the effectiveness of the proposed P system.