Computation with a constant number of steps in membrane computing.

Abstract

In the present paper, we propose P systems that work in a constant number of steps. We first propose two P systems for computing multiple input logic functions. An input of the logic functions is a set of n binary numbers of m bits, and an output is a binary number defined by the logic functions. The first and second P systems compute AND and EX-OR functions for the input, and both of the P systems work in a constant number of steps using O(mn) types of objects, a constant number of membranes, and evolution rules of size O(mn). Next, we propose the P system for the addition of two binary numbers of m bits. The P system works in a constant number of steps using O(m) types of objects, a constant number of membranes and evolution rules of size O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). We also introduce a P system that computes the addition of two vectors of size n using the above P system as a sub-system. The P system for vector addition works in a constant number of steps using O(mn) types of objects, a constant number of membranes, and evolution rules of size O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> n).