Asynchronous SN P Systems for Sorting

We propose two kinds of asynchronous SN P systems for sorting. We first propose an anynchronous SN P system that works as a comparator, which sorts two binary numbers of m bits. The SN P systems work in O(m) sequential steps or O(log m) parallel steps using O(m) neurons. We next propose an asynchronous SN P system that simulates a sorting network, which sorts n binary numbers of m bits using the above comparator. The SN P system works in O(mn log n) sequential steps or O(log m log n) parallel steps using O(mn log n) neurons. Finally, we propose another SN P system that sorts n binary numbers of m bits. The SN P system is based on a round robin tournament, and works in O(mn²) sequential steps or O(log m) parallel steps using O(mn²) neurons.