Abstract
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.
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References
A. Alhazov: Minimizing Evolution-Communication P Systems and Automata. New Generation Computing, 22,4, (2004), 299–310.
A. Alhazov, D. Sburlan: Static Sorting Algorithms for P Systems. In Pre-Proceedings of the Workshop on Membrane Computing, Tarragona, 2003 (A. Alhazov, C. Martín-Vide, Gh. Păun, eds.), GRLMC Report 28/03, Tarragona, 2003, 17–40.
J.J. Arulanandham: Implementing Bead-Sort with P Systems. In Unconventional Models of Computation 2002 (C.S. Calude, M.J. Dinneen, F. Peper, eds.), LNCS 2509, Springer, Berlin, 2002, 115–125.
M. Cavaliere: Evolution-Communication P Systems. In Membrane Computing, International Workshop, WMC-CdeA 2002, Curtea de Argeş, Romania, August 2002, Revised Papers (Gh. Păun, G. Rozenberg, A. Salomaa, C. Zandron, eds.), LNCS 2597, Springer, Berlin, 2003, 134–145.
R. Ceterchi, C. Martín-Vide: P Systems with Communication for Static Sorting. In Pre-Proceedings of Brainstorming Week on Membrane Computing, Tarragona, February 2003 (M. Cavaliere, C. Martín-Vide, Gh. Păun, eds.), Tech. Rep. No. 26, Rovira i Virgili Univ., Tarragona, 2003.
R. Freund, L. Kari, M. Oswald, P. Sosik: Computationally Universal P Systems Without Priorities: Two Catalysts Are Sufficient. Theoretical Computer Science, 330,2 (2005), 251–266.
M. Ionescu, D. Sburlan: On P Systems with Promoters/Inhibitors. Journal of Universal Computer Science, 10,5, (2004), 581–599.
S.N. Krishna, A. Păun: Three Universality Results on P Systems. In Pre-Proceedings of Brainstorming Week on Membrane Computing, Tarragona, February 2003 (M. Cavaliere, C. Martín-Vide, Gh. Păun, eds.), Tech. Rep. No. 26/03, Rovira i Virgili Univ., Tarragona, 2003, 198–206.
Gh. Păun: Membrane Computing. An Introduction. Springer, Berlin, 2002.
D. Sburlan: A Static Sorting Algorithm for P Systems with Mobile Catalysts. Analele Ştiintifice Univ. Ovidius Constanţa, seria Matematică, 11,1, (2003), 195–205.
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Alhazov, A., Sburlan, D. (2006). Static Sorting P Systems. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds) Applications of Membrane Computing. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29937-8_8
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DOI: https://doi.org/10.1007/3-540-29937-8_8
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