Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Automata, Languages, and Programming

ICALP 2003: Automata, Languages and Programming pp 267–277Cite as

Sophistication Revisited

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

Abstract

The Kolmogorov structure function divides the smallest program producing a string in two parts: the useful information present in the string, called sophistication if based on total functions, and the remaining accidental information. We revisit the notion of sophistication due to Koppel, formalize a connection between sophistication and a variation of computational depth (intuitively the useful or nonrandom information in a string), prove the existence of strings with maximum sophistication and show that they encode solutions of the halting problem, i.e., they are the deepest of all strings.

Research done during an academic internship at NEC. This author is partially supported by funds granted to LIACC through the Programa de Financiamento Plurianual, Fundação para a Ciência e Tecnologia and Programa POSI.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Antunes. Useful Information. PhD Thesis, Computer Science Department, Oporto University, 2002.

    Google Scholar 

  2. Luis Antunes, Lance Fortnow, and Dieter van Melkebeek. Computational depth. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 266–273, 2001.

    Google Scholar 

  3. C. H. Bennett. Logical depth and physical complexity. In R. Herken, editor, The Universal Turing Machine: A Half-Century Survey, pages 227–257. Oxford University Press, 1988.

    Google Scholar 

  4. T. M. Cover. Kolmogorov Complexity, Data Compression, and Inference, pp. 23–33. In The Impact of Processing Techniques on Communications. J. K. Skwirzynski, Ed., Martinus Nijhoff Publishers, 1985.

    Google Scholar 

  5. Robert P. Daley Busy Beaver Sets: Characterizations and Applications. In Information and Control, 52(1982), 52–67.

    Article  MATH  MathSciNet  Google Scholar 

  6. Peter Gács and John Tromp and Paul Vitányi. Algorithmic Statistics. In IEEE Trans. Inform. Theory, 47:6(2001), 2443–2463.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Koppel. Structure, pp. 435–452. In The Universal Turing Machine: A Half-Century Survey. R. Herken, Ed., Oxford University Press, 1988.

    Google Scholar 

  8. M. Koppel. Learning to Predict Non-Deterministically Generated Strings. Machine Learning, 7(1991), 85–99.

    MATH  Google Scholar 

  9. M. Koppel and H. Atlan. An Almost Machine-Independent Theory of Program-Length Complexity, Sophistication, and Induction. Information Sciences, 56(1991), 23–33.

    Article  MATH  MathSciNet  Google Scholar 

  10. Leonid A. Levin. Universal Search Problems. Problems Inform. Transmission, 9(1973), 265–266.

    Google Scholar 

  11. Leonid A. Levin. Randomness conservation inequalities: information and independence in mathematical theories. Information and Control, 61:15–37, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  12. Ming Li and Paul M. B. Vitányi. An introduction to Kolmogorov complexity and its applications. Springer, 2nd edition, 1997.

    Google Scholar 

  13. C. P. Schnorr. Process Complexity and Effective Random Tests. J. Comp. System Sci., 7(1973), 376–388.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Kh. Shen. The Concept of (α, β)-Stochasticity in the Kolmogorov Sense, and its Properties. Soviet Math. Dokl., 28(1983), 295–299.

    MATH  Google Scholar 

  15. N. Vereshchagin and P. Vitányi. Kolmogorov’s structure functions and an application to the foundations of model selection. Proc. 47th IEEE Symp. Found. Comput. Sci., 2002.

    Google Scholar 

  16. P. Vitányi. Meaningful information. Proc. 13th International Symposium on Algorithms and Computation (ISAAC’02). Lecture Notes in Computer Science, Vol 2518, Springer-Verlag, Berlin, 2002, 588–599.

    Google Scholar 

  17. V.V. V’yugin. Algorithmic complexity and stochastic properties of finite binary sequences. The Computer Journal, 42(4):294–317, 1999.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DCC-FC & LIACC-University of Porto, R.Campo Alegre, 823, 4150-180, Porto, Portugal

    Luís Antunes

  2. NEC Laboratories America, 4 Independence way, Princeton, NJ, 08540

    Lance Fortnow

Authors
  1. Luís Antunes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lance Fortnow
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Antunes, L., Fortnow, L. (2003). Sophistication Revisited. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-45061-0_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation