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Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem

Received: 26 February 2017     Accepted: 26 April 2017     Published: 23 October 2017
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Abstract

In paper are considered laws of functioning of discrete determined dynamical systems and specific processes of functioning of such systems. As basic mathematical model of laws of functioning of systems are used automata models with a fundamentally new extension of these models to models with a countable infinite sets of states. This expansion is possible thanks to the proposed and developed by Tverdohlebov V. A. the mathematical apparatus of geometrical images of automaton mappings. Are presented results of development of regularization methods for partially set automata models of systems based on use of geometrical images of automatons mappings and numerical interpolation methods. Also in paper are considered a problem of complexity estimation of laws in a whole and specific processes of functioning of dynamic systems. For these purpose are used recurrent models and methods and also a specific mathematical apparatus of discrete riv-functions. Is spent classification by complexity estimations of automata models.

Published in American Journal of Management Science and Engineering (Volume 2, Issue 5)
DOI 10.11648/j.ajmse.20170205.14
Page(s) 106-116
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Discrete Dynamical System, Mathematical Model, Automata Model, Geometrical Image of Automaton, Recurrent Model, Interpolation, Discrete Riv-Function

References
[1] E. Moore, "Gedanken-experiments on sequential machines", collection: Automata Studies, ed. C. E. Shannon and J. McCarthy [Russian translation], IL. 1956.
[2] A. Gill, "Introduction to the Theory of Finite-state Machines". McGraw-Hill, 1962.
[3] T. N. Hibbard, "Exact upper bounds for lengths of minimal experiments to determine the final state, for two classes of sequential machines", in: Cybernetics Collection, No. 2, In. Lit., Moscow, 1966.
[4] V. A. Tverdokhlebov, "The geometrical images of laws of functioning of finite state machines". Science book, Saratov, 2008.
[5] V. A. Tverdohlebov, A. S. Epifanov, "Representation of automatons by geometrical structures", Publishing Center Science, Saratov, 2013.
[6] M. Sipser, "The history and status of the P versus NP question". Proceeding of 24th annual symposium on the theory of computing, 1994.
[7] R. Hofman, "Complexity considerations", cSAT lower bound. IMECS2007, Conference proceedings published by IAENG, 2007.
[8] M. Li, P. Vitanyi, "Introduction to Kolmogorov сomplexity and its applications". Springer-verilag, 1993.
[9] A. Borodin, I. Munro, "The computational complexity of algebraic and numeric problems". American Elsevier, New York, 1975.
[10] H. Khalil, D. Ulery, "A review of current studies on complexity of algorithms for partial differential equations". ACM '76 proceedings of the 1976 annual conference, 1976.
[11] L. Fortnow, S. Homer, "A short history of computational complexity". Bulletin of the EATCS 80, 2003.
[12] Y. Kartynnik, A. Ryzhikov, "On minimum maximal distance-k matchings". Electronic notes in discrete mathematics, 2016, V. 56, PP. 71-76.
[13] V. Lozin, С. Purcell, R. Mosca, "Independent domination in finitely defined classes of graphs: polynomial algorithms", Discrete applied mathematics, 2015, V. 182, PP. 2-14.
[14] F. Foucaud, "Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes", Journal of discrete algorithms. 2015, V. 31, PP. 48-68.
[15] http://www.oeis.org.
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  • APA Style

    Anton S. Epifanov. (2017). Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem. American Journal of Management Science and Engineering, 2(5), 106-116. https://doi.org/10.11648/j.ajmse.20170205.14

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    ACS Style

    Anton S. Epifanov. Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem. Am. J. Manag. Sci. Eng. 2017, 2(5), 106-116. doi: 10.11648/j.ajmse.20170205.14

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    AMA Style

    Anton S. Epifanov. Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem. Am J Manag Sci Eng. 2017;2(5):106-116. doi: 10.11648/j.ajmse.20170205.14

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  • @article{10.11648/j.ajmse.20170205.14,
      author = {Anton S. Epifanov},
      title = {Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem},
      journal = {American Journal of Management Science and Engineering},
      volume = {2},
      number = {5},
      pages = {106-116},
      doi = {10.11648/j.ajmse.20170205.14},
      url = {https://doi.org/10.11648/j.ajmse.20170205.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmse.20170205.14},
      abstract = {In paper are considered laws of functioning of discrete determined dynamical systems and specific processes of functioning of such systems. As basic mathematical model of laws of functioning of systems are used automata models with a fundamentally new extension of these models to models with a countable infinite sets of states. This expansion is possible thanks to the proposed and developed by Tverdohlebov V. A. the mathematical apparatus of geometrical images of automaton mappings. Are presented results of development of regularization methods for partially set automata models of systems based on use of geometrical images of automatons mappings and numerical interpolation methods. Also in paper are considered a problem of complexity estimation of laws in a whole and specific processes of functioning of dynamic systems. For these purpose are used recurrent models and methods and also a specific mathematical apparatus of discrete riv-functions. Is spent classification by complexity estimations of automata models.},
     year = {2017}
    }
    

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    AB  - In paper are considered laws of functioning of discrete determined dynamical systems and specific processes of functioning of such systems. As basic mathematical model of laws of functioning of systems are used automata models with a fundamentally new extension of these models to models with a countable infinite sets of states. This expansion is possible thanks to the proposed and developed by Tverdohlebov V. A. the mathematical apparatus of geometrical images of automaton mappings. Are presented results of development of regularization methods for partially set automata models of systems based on use of geometrical images of automatons mappings and numerical interpolation methods. Also in paper are considered a problem of complexity estimation of laws in a whole and specific processes of functioning of dynamic systems. For these purpose are used recurrent models and methods and also a specific mathematical apparatus of discrete riv-functions. Is spent classification by complexity estimations of automata models.
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Author Information
  • Department of Control Problems of Automation Engineering, Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, Russia

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