Enzymatic numerical P systems for basic operations and sorting

Membrane computing, which is a computational model inspired by the structures and behaviors of living cells, has considerable attention as one of non-silicon based computing. In the present paper, we propose EN P systems for basic operations, and sorting. We first propose three EN P systems for computing three logic operations, OR, AND, and EX-OR functions. All of the EN P systems work in a constant number of steps. Next, we propose two EN P systems that operates as a half adder and a full adder, and then, propose two EN P system for additions of two binary numbers and n binary numbers. We show the EN P systems for two additions work in O(m) steps and O(nm) steps, respectively. Finally, we propose two EN P systems for sorting. We propose an EN P system for compare-and-exchange operation. Then, using the EN P system as sub-systems, we propose an EN P system for sorting n numbers, and show that the EN P system works in O(n) steps.