Static Sorting P Systems Artiom Alhazov ⋆1,2 and Drago¸ s Sburlan ⋆⋆1,3 1 Research Group on Mathematical Linguistics Rovira i Virgili University Pl. Imperial T`arraco 1, 43005 Tarragona, Spain 2 Institute of Mathematics and Computer Science Academy of Sciences of Moldova Str. Academiei 5, Chi¸ sin˘au, MD 2028, Moldova E-mail: artiom@math.md 3 Faculty of Mathematics and Computer Science Ovidius University of Constant ¸a Bd. Mamaia 120, Constant ¸a, Romania E-mail: dsburlan@univ-ovidius.ro Abstract. The topic of this chapter is application of P systems for sort- ing problems, i.e., constructing sorting algorithms for various variants of P systems. Traditional studies of sorting assume a constant time for com- paring two numbers and compute the time complexity with respect to the number of components of a vector to be sorted. Here we assume the num- ber of components to be a fixed number k, and study various algorithms with distinct generative features based on different models of P systems, and their time complexity with respect to the maximal number, or to their sum. Massively parallel computations that can be realized within the framework of P systems offer a premise to major improvements of 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 the com- plexity “comparable” with the classical integer sorting algorithms. Still, computing an (ordered) word from an (unordered) multiset can be a goal not only for computer science but also, at least, for bio-synthesis (sep- arating mixed objects according to some characteristics). Here, we will pass from ranking algorithms that, starting with numbers represented as multisets, produce symbols in an order, to effective sorting algorithms. Keywords: Static Sorting, Ranking, P Systems ⋆ The first author is supported by the project TIC2002-04220-C03-02 of the Research Group on Mathematical Linguistics, Tarragona. The first author acknowledges IST- 2001-32008 project “MolCoNet” and also the Moldovan Research and Development Association (MRDA) and the U.S. Civilian Research and Development Foundation (CRDF), Award No. MM2-3034. ⋆⋆ The second author’s work was supported by a doctoral fellowship from Agencia Espa˜ nola de Cooperaci´on Internacional, Spanish Ministry of Foreign Affairs.