Skip to main content
SpringerLink
Log in

The Search for the Universal Concept of Complexity and a General Optimality Condition of Cooperative Agents

  • Chapter
Cooperative Control: Models, Applications and Algorithms

Part of the book series: Cooperative Systems ((COSY,volume 1))

Abstract

There are many different notions of complexity. However, complexity does not have a generally accepted universal concept. It is becoming more clear that the search for the universal concept must be done within a final theory. In this chapter a concept of structural complexity for the first time suggests the real opportunity to search the universal concept of complexity within a final theory. Experimental facts given in this chapter allow to suggest a general optimality condition of cooperative agents in terms of structural complexity. The optimality condition says that cooperative agents show their best performance for a particular problem when their structural complexity equals the structural complexity of the problem. According to the optimality condition to control a complex system efficiently means to equate its structural complexity with the structural complexity of the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Bennett, “On the nature and origin of complexity in discrete, homogeneous, locally-interacting systems”, Foundations of Physics, 16:585–592, 1986.

    Article  MathSciNet  Google Scholar 

  2. L. Brillouin, Science and Information Theory, Academic, London, 1962.

    MATH  Google Scholar 

  3. G. J. Chaitin, “On the length of programs for computing binary sequences”, Journal of ACM, 13: 547–569, 1966.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. J. Chaitin, Exploring Randomness, Springer-Verlag, 2001.

    Book  MATH  Google Scholar 

  5. J. P. Crutchfield, “The calculi of emergence”, Physica D, 75: 11–54, 1994.

    Article  MATH  Google Scholar 

  6. H. C. Fogedby, 7. Stat. Phys., 69: 411, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP Completeness, Freeman, San Franisco, 1979.

    MATH  Google Scholar 

  8. M. Gell-Mann, The Quark and the Jaguar: Adventures in the Simple and Complex, W. H. Freeman and Company, New York, 1994.

    MATH  Google Scholar 

  9. M. Gell-Mann and S. Lloyd, Complexity, 2: 44, 1996.

    Article  MathSciNet  Google Scholar 

  10. P. Grassberger, Int. J. Theor. Phys., 25: 907, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. P. Crutchfield and D. P. Feldman, Phys. Rev. E, 55: 1239, 1997.

    Article  Google Scholar 

  12. J. H. Holland, Hidden Order: How Adaptation Builds Complexity, Addison-Wesley, Reading, MA, 1995.

    Google Scholar 

  13. J. H. Holland, Emergence: From Chaos to Order, Perseus Books, Reading, Massachusetts, 1998.

    Google Scholar 

  14. J. Horgan, The End of Science, Broadway Books, New York, 1996.

    MATH  Google Scholar 

  15. B. A. Huberman and T. Hogg, Physica D, 22: 376, 1986.

    MathSciNet  Google Scholar 

  16. S. Kauffman, At Home in the Universe: the Search for Laws of Self-organization and Complexity, Oxford University Press, New York, 1995.

    Google Scholar 

  17. A. Kolmogorov, “Three approaches to the definition of the concept ‘Quantity of Information’”, Problems of Information Transmission, 1: 1–7, 1965.

    Google Scholar 

  18. N. M. Korobov, Trigonometric Sums and their Applications, Nauka, Moscow, 1989.

    MATH  Google Scholar 

  19. V. Korotkich, A Mathematical Structure for Emergent Computation, Kluwer Academic Publishers, 1999.

    MATH  Google Scholar 

  20. V. Korotkich, “On complexity and optimization in emergent computation”, In P. Pardalos, editor, Approximation and Complexity in Numerical Optimization, pp. 347–363, Kluwer Academic Publishers, 2000.

    Google Scholar 

  21. V. Korotkich, “On optimal algorithms in emergent computation”, In A. Rubinov and B. Glover, editors, Optimization and Related Topics, pp. 83–102, Kluwer Academic Publishers, 2001.

    Google Scholar 

  22. V. Korotkich, “On self-organization of cooperative systems and fuzzy logic”, In V. Dimitrov and V. Korotkich, editors, Fuzzy Logic: A Framework for the New Millennium, pp. 147–167, Springer-Verlag, 2002.

    Google Scholar 

  23. R. Landauer, IBM J. Res. Dev. 3: 183, 1961.

    Article  MathSciNet  Google Scholar 

  24. C. Langton, Physica D, 42: 12, 1990.

    Article  MathSciNet  Google Scholar 

  25. M. Li and P. Vitanyi, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, 1997.

    Book  MATH  Google Scholar 

  26. S. Lloyd and H. Pagels, “Complexity as thermodynamic depth”, Annals of Physics, 188: 186–213, 1988.

    Article  MathSciNet  Google Scholar 

  27. P. G. Mezey, Potential Energy Hypersurfaces, Elsevier, Amsterdam, 1987.

    Google Scholar 

  28. L. Mordell, “On a sum analogous to a Gauss’ sum”, Quart. J. Math., 3: 161–167, 1932.

    Article  MATH  Google Scholar 

  29. M. Morse, “Recurrent geodesics on a surface of negative curvature”, Trans. Amer. Math. Soc, 22: 84, 1921.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Nadeau and M. Kafatos. The Non-local Universe, Oxford University Press, New York, 2001.

    Google Scholar 

  31. G. Nicolis and I. Prigogine, Exploring Complexity, New York, Freeman, 1989.

    Google Scholar 

  32. C. Papadimitriou, Computational Complexity, Addison-Wesley, Reading, MA, 1994.

    MATH  Google Scholar 

  33. A.S. Perelson and S.A. Kauffman, editors, Molecular Evolution on Rugged Landscapes: Proteins, RNA, and the Immune System, vol. 9 of Santa Fe Studies, Reading, MA, Addison-Wesley, 1991.

    Google Scholar 

  34. E. Prouhet, “Memoire sur quelques relations entre les puissances des nombres”, CR. Acad. Sci., Paris, 33: 225, 1851.

    Google Scholar 

  35. S. Ramanujan, “Note on a set of simultaneous equations”, J. Indian Math. Soc, 4: 94–96, 1912.

    MATH  Google Scholar 

  36. G. Reinelt, TSPLIB 1.2 [Online] Available from: URL ftp://ftp.wiwi.uni-frankfurt.de/pub/TSPLIB 1.2, 2000.

  37. C. E. Shannon, “A mathematical theory of communication”, Bell System Technical Journal, July and October, 1948,

    Google Scholar 

  38. C. E. Shannon, “A mathematical theory of communication”, reprinted in C. E. Shannon and W. Weaver, editors, A Mathematical Theory of Communication, University of Illinois Press, Urbana, 1949.

    Google Scholar 

  39. R. Solomonoff, “A formal theory of inductive inference”, Information and Control, 7:1–22, 1964.

    Article  MathSciNet  MATH  Google Scholar 

  40. L. Szilard, Z Phys., 53: 840, 1929.

    Article  MATH  Google Scholar 

  41. A. Thue, “Uber unendliche zeichenreihen”, Norske vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana, 7: 1, 1906.

    Google Scholar 

  42. J. Traub, G. Wasilkowski and H. Wozniakowski, Information-based Complexity, Academic Press, 1988.

    MATH  Google Scholar 

  43. S. Weinberg, Dreams of a Final Theory, Pantheon, New York, 1992.

    Google Scholar 

  44. H. Weyl, “Uber die gleichverteilung von zahlen mod”, Eins. Math. Ann., 77: 313–352, 1915/16.

    Article  MathSciNet  Google Scholar 

  45. J. A. Wheeler, A Journey into Gravity and Spacetime, Scientific American Library, New York, 1990.

    Google Scholar 

  46. E. Witten, “Reflections on the fate of spacetime”, Physics Today, 49: 24–30, 1996.

    Article  MathSciNet  Google Scholar 

  47. S. Wolfram, Cellular automata and complexity, Addison-Wesley, 1994.

    MATH  Google Scholar 

  48. W. H. Zurek, “Algorithmic randomness and physical entropy”, Physical Review A, 40: 4731–4751, 1989.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Informatics and Communication, Central Queensland University, Mackay, Queensland, 4740, Australia

    Victor Korotkich

Authors
  1. Victor Korotkich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, Florida, USA

    Sergiy Butenko  & Panos M. Pardalos  & 

  2. Air Force Research Laboratory, Eglin AFB, Florida, USA

    Robert Murphey

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Korotkich, V. (2003). The Search for the Universal Concept of Complexity and a General Optimality Condition of Cooperative Agents. In: Butenko, S., Murphey, R., Pardalos, P.M. (eds) Cooperative Control: Models, Applications and Algorithms. Cooperative Systems, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3758-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3758-5_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5241-7

  • Online ISBN: 978-1-4757-3758-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation