Abstract
A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied to certain positions in a string. An HNEP rewrites the strings in the nodes and then re-distributes them according to a filter-based communication protocol; the filters are defined by certain variants of random-context conditions. HNEPs can be considered both as languages generating devices (GHNEPs) and language accepting devices (AHNEPs); most previous approaches treated the accepting and generating cases separately. For both cases, in this paper we improve previous results by showing that five nodes are sufficient to accept (AHNEPs) or generate (GHNEPs) any recursively enumerable language by showing the more general result that any partial recursive relation can be computed by an HNEP with (at most) five nodes.
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References
Alhazov, A., Csuhaj-Varjú, E., Martín-Vide, C., Rogozhin, Y.: About Universal Hybrid Networks of Evolutionary Processors of Small Size. In: LATA 2008. LNCS, vol. 5196, pp. 28–39. Springer, Heidelberg (2008)
Alhazov, A., Csuhaj-Varjú, E., Martín-Vide, C., Rogozhin, Y.: Computational Completeness of Hybrid Networks of Evolutionary Processors with Seven Nodes. In: Campeanu, C., Pighizzini, G. (eds.) Descriptional Complexity of Formal Systems, Proceedings DCFS 2008, Univ. Prince Edward Island, Charlottetown, pp. 38–47 (2008)
Alhazov, A., Csuhaj-Varjú, E., Martín-Vide, C., Rogozhin, Y.: On the Size of Computationally Complete Hybrid Networks of Evolutionary Processors. Theoretical Computer Science 410, 3188–3197 (2009)
Alhazov, A., Dassow, J., Martín-Vide, C., Rogozhin, Y., Truthe, B.: On Networks of Evolutionary Processors with Nodes of Two Types. Fundamenta Informaticae 91(1), 1–15 (2009)
Alhazov, A., Krassovitskiy, A., Rogozhin, Y.: Circular Post Mahines and P Systems with Exo-insertion and Deletion. In: Gheorghe, M., Păun, G., Rozenberg, G., Salomaa, A., Verlan, S. (eds.) CMC 2011. LNCS, vol. 7184, pp. 73–86. Springer, Heidelberg (2012)
Alhazov, A., Kudlek, M., Rogozhin, Y.: Nine Universal Circular Post Machines. Computer Science Journal of Moldova 10(3), 247–262 (2002)
Alhazov, A., Martín-Vide, C., Rogozhin, Y.: On the Number of Nodes in Universal Networks of Evolutionary Processors. Acta Inf. 43(5), 331–339 (2006)
Alhazov, A., Martín-Vide, C., Rogozhin, Y.: Networks of Evolutionary Processors with Two Nodes are Unpredictable. In: Pre-Proceedings of the 1st International Conference on Language and Automata Theory and Applications, LATA, GRLMC report 35/07, Rovira i Virgili University, Tarragona, 521–528 (2007)
Castellanos, J., Leupold, P., Mitrana, V.: On the Size Complexity of Hybrid Networks of Evolutionary Processors. Theoretical Computer Science 330(2), 205–220 (2005)
Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.M.: Solving NP-complete Problems with Networks of Evolutionary Processors. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 621–628. Springer, Heidelberg (2001)
Csuhaj-Varjú, E., Martín-Vide, C., Mitrana, V.: Hybrid Networks of Evolutionary Processors are Computationally Complete. Acta Inf. 41(4-5), 257–272 (2005)
Freund, R., Rogozhin, Y., Verlan, S.: Generating and Accepting P Systems with Minimal Left and Right Insertion and Deletion. Natural Computing. Springer (2014), doi:10.1007/s11047-013-9396-3
Kudlek, M., Rogozhin, Y.: Small Universal Circular Post Machines. Computer Science Journal of Moldova 9(1), 34–52 (2001)
Kudlek, M., Rogozhin, Y.: New Small Universal Circular Post Machines. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 217–227. Springer, Heidelberg (2001)
Loos, R., Manea, F., Mitrana, V.: Small Universal Accepting Hybrid Networks of Evolutionary Processors. Acta Informatica 47(2), 133–146 (2010)
Manea, F., Martín-Vide, C., Mitrana, V.: On the Size Complexity of Universal Accepting Hybrid Networks of Evolutionary Processors. Mathematical Structures in Computer Science 17(4), 753–771 (2007)
Manea, F., Martín-Vide, C., Mitrana, V.: All NP-problems can be Solved in Polynomial Time by Accepting Hybrid Networks of Evolutionary Processors of Constant Size. Information Processing Letters 103, 112–118 (2007)
Margenstern, M., Mitrana, V., Jesús Pérez-Jímenez, M.: Accepting Hybrid Networks of Evolutionary Processors. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 235–246. Springer, Heidelberg (2005)
Martín-Vide, C., Mitrana, V., Pérez-Jiménez, M.J., Sancho-Caparrini, F.: Hybrid Networks of Evolutionary Processors. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 401–412. Springer, Heidelberg (2003)
Post, E.L.: Formal Reductions of the General Combinatorial Decision Problem. American Journal of Mathematics 65(2), 197–215 (1943)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer (1997)
Salomaa, A.: Formal Languages. Academic Press, New York (1973)
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Alhazov, A., Freund, R., Rogozhin, Y. (2014). Five Nodes Are Sufficient for Hybrid Networks of Evolutionary Processors to Be Computationally Complete. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_1
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DOI: https://doi.org/10.1007/978-3-319-08123-6_1
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