Abstract
In this paper we show that some aspects of networks of evolutionary processors can be normalized or simplified without loosing generative power. More precisely, we show that one can use very small finite automata for the control of the communication. We first prove that the networks with evolutionary processors remain computationally complete if one restricts the control automata to have only one state, but underlying graphs of the networks have no fixed structure and the rules are applied in three different modes. Moreover, we show that networks where the rules are applied arbitrary, and all the automata for control have one state, cannot generate all recursively enumerable languages. Finally, we show that one can generate all recursively enumerable languages by complete networks, where the rules are applied arbitrary, but the automata for control have at most two states.
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References
Hillis, W.D.: The Connection Machine. MIT Press, Cambridge (1986)
Errico, L.D., Jesshope, C.: Towards a New Architecture for Symbolic Processing. In: Proc. of AIICSR 1994, pp. 31–40. World Scientific Publishing Co., Inc., River Edge (1994)
Fahlman, S.E., Hinton, G.E., Sejnowski, T.J.: Massively Parallel Architectures for AI: NETL, Thistle, and Boltzmann Machines. In: Proc. AAAI 1983, pp. 109–113 (1983)
Csuhaj-Varjú, E., Salomaa, A.: Networks of Parallel Language Processors. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 299–318. Springer, Heidelberg (1997)
Csuhaj-Varjú, E., Mitrana, V.: Evolutionary Systems: A Language Generating Device Inspired by Evolving Communities of Cells. Acta Informatica 36(11), 913–926 (2000)
Păun, G.: Computing with Membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)
Păun, G., Sântean, L.: Parallel Communicating Grammar Systems: The Regular Case. Annals of University of Bucharest, Ser. Matematica-Informatica 38, 55–63 (1989)
Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.M.: Networks of evolutionary processors. Acta Informatica 39(6-7), 517–529 (2003)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, F., Cedergren, R.: Gene Order Comparisons for Phylogenetic Inference: Evolution of the Mitochondrial Genome. Proc. of the National Academy of Sciences of the United States of America 89(14), 6575–6579 (1992)
Martín-Vide, C., Mitrana, V.: Networks of evolutionary processors: Results and perspectives. In: Molecular Computational Models: Unconventional Approaches, pp. 78–114 (2005)
Alhazov, A., Dassow, J., Martín-Vide, C., Rogozhin, Y., Truthe, B.: On networks of evolutionary processors with nodes of two types. Fundamenta Informaticae 91, 1–15 (2009)
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)
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)
Dassow, J., Manea, F., Truthe, B.: A Normal Form for Networks of Evolutionary Processors. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2010), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2010-02.pdf
Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer, Heidelberg (1997)
Geffert, V.: Normal forms for phrase-structure grammars. RAIRO – Theoretical Informatics and Applications 25, 473–496 (1991)
Dassow, J., Manea, F., Truthe, B.: Networks of Evolutionary Processors with Subregular Filters. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2011), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2011-01.pdf
Dassow, J., Truthe, B.: On networks of evolutionary processors with filters accepted by two-state-automata (submitted)
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Dassow, J., Manea, F., Truthe, B. (2011). On Normal Forms for Networks of Evolutionary Processors. In: Calude, C.S., Kari, J., Petre, I., Rozenberg, G. (eds) Unconventional Computation. UC 2011. Lecture Notes in Computer Science, vol 6714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21341-0_14
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DOI: https://doi.org/10.1007/978-3-642-21341-0_14
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