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Tytuł artykułu

Maximizing T-complexity

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Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
We investigate Mark Titchener’s T-complexity, an algorithm which measures the information content of finite strings. After introducing the T-complexity algorithm, we turn our attention to a particular class of “simple” finite strings. By exploiting special properties of simple strings, we obtain a fast algorithm to compute the maximum T-complexity among strings of a given length, and our estimates of these maxima show that T-complexity differs asymptotically from Kolmogorov complexity. Finally, we examine how closely de Bruijn sequences resemble strings with high Tcomplexity.
Wydawca
Rocznik
Strony
1--19
Opis fizyczny
Bibliogr. 23 poz., tab.
Twórcy
autor
  • U.S. Department of Defense Washington, DC 20301-1400, USA
autor
  • Penn State University University Park, PA 16082, USA
Bibliografia
  • [1] van Aardenne-Ehrenfest, T., de Bruijn, N. G.: Circuits and trees in oriented linear graphs, Simon Stevin, 28, 1951, 203–217, ISSN 0037-5454.
  • [2] Calude, C. S., Salomaa, K., Roblot, T. K.: Finite-State Complexity and Randomness, Technical Report 374, University of Auckland CDMTCS Research Report Series, December 2009.
  • [3] Chebolu, S. K.,Min´aˇc, J.: Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle, Mathematics Magazine, 84(5), 2011, 369–371.
  • [4] Eimann, R., Speidel, U., Brownlee, N., Yang, J.: Network Event Detection with T-Entropy, CDMTCS Research Report Series, 266, 2005.
  • [5] Eimann, R. E. A.: Network event detection with entropy measures, Ph.D. Thesis, The University of Auckland, 2008.
  • [6] Gulliver, T. A.,Makwakwa, I., Speidel, U.: On the Generation of Aperiodic and Periodic Necklaces via T-augmentation, Fundamenta Informaticae, 83(1-2), 2008, 91–107, ISSN 0169-2968.
  • [7] Hamano, K., Yamamoto, H.: A differential equation method to derive the formulas of the Tcomplexity and the LZ-complexity, Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1, ISIT 2009, IEEE Press, Piscataway, NJ, USA, 2009, ISBN 978-1-4244-4312-3.
  • [8] Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory, Number 84 in Graduate Texts in Mathematics, second edition, Springer-Verlag, New York, 1990, ISBN 0-387-97329X.
  • [9] Lempel, A., Ziv, J.: On the complexity of finite sequences, IEEE Transactions on Information Theory, IT-22(1), 1976, 75–81, ISSN 0018-9448.
  • [10] Li, M., Vit´anyi, P.: An introduction to Kolmogorov complexity and its applications, Texts in Computer Science, third edition, Springer, New York, 2008, ISBN 978-0-387-33998-6.
  • [11] Li, M., Vitányi, P. M. B.: Statistical properties of finite sequences with high Kolmogorov complexity, Mathematical Systems Theory, 27(4), 1994, 365–376, ISSN 0025-5661.
  • [12] Matoušek, J., Nešetřil, J.: Invitation to discrete mathematics, Second edition, Oxford University Press, Oxford, 2009, ISBN 978-0-19-857042-4.
  • [13] Moreau, C.: Sur les permutations circulaires distinctes, Nouvelles annalles de mathématiques, 2(11), 1872, 309–314.
  • [14] Niven, I., Zuckerman, H. S., Montgomery, H. L.: An introduction to the theory of numbers, Fifth edition, John Wiley & Sons Inc., New York, 1991, ISBN 0-471-62546-9.
  • [15] Speidel, U.: T-Complexity and T-Information Theory–an Executive Summary, 2nd revised version, Technical Report 286, University of Auckland CDMTCS Research Report Series, October 2006.
  • [16] Speidel, U.: On the bounds of the Titchener T-complexity, Proceedings of Communication Systems, Networks and Digital Signal Processing 2008, CNSDSP 2008, July 2008.
  • [17] Titchener, M. R.: Digital encoding by means of new T-codes to provide improved data synchronization and message integrity, July 1984, Technichal note.
  • [18] Titchener, M. R., Nicolescu, R., Staiger, L., Gulliver, A., Speidel, U.: Deterministic Complexity and Entropy, Fundamenta Informaticae, 64(1-4), 2004, 443–461, ISSN 0169-2968.
  • [19] Welch, T. A.: A Technique for High-Performance Data Compression, Computer, 17(6), june 1984, 8–19, ISSN 0018-9162.
  • [20] Xie, S. Q.: Notes on de Bruijn sequences, Discrete Applied Mathematics, 16(2), 1987, 157–177, ISSN 0166-218X.
  • [21] Ziv, J., Lempel, A.: A universal algorithm for sequential data compression, IEEE Transactions on Information Theory, 23(3), may 1977, 337–343, ISSN 0018-9448.
  • [22] Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding, IEEE Transactions on Information Theory, 24(5), september 1978, 530–536, ISSN 0018-9448.
  • [23] Zvonkin, A. K., Levin, L. A.: The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms., Russian Mathematical Surveys, 25(6), 1970, 83–124.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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