Static Sorting P Systems

This chapter deals with the application of P systems to sorting problems. Traditional studies of sorting assume constant time for comparing two numbers and compute the time complexity with respect to the number of components of a vector to be sorted. Here, we assume the number of components to be a fixed number

k

, and study various algorithms based on different models of P systems and their time complexities with respect to the maximal number or to the sum of the numbers. Massively parallel computations that can be realized within the framework of P systems may lead to major improvements in solving the classical integer sorting problems. Despite this important characteristic, we will see that, depending on the model used, the massive parallelism feature cannot be always used, and so some results will have complexities “comparable” with the classical integer sorting algorithms. Still, computing a word (ordered) from a multiset (unordered) can be a goal not only for computer science, but also, e.g., for biosynthesis (separating mixed objects according to some characteristics). Here, we will move from ranking algorithms that, starting with numbers represented as multisets, produce symbols in an order, to effective sorting algorithms.