Skip to main content

Reconstructing Language Hierarchies

  • Chapter
Information Dynamics

Part of the book series: NATO ASI Series ((NSSB,volume 256))

Abstract

Within an assumed language class optimal models can be estimated using Gibb-sian statistical mechanics. But how are model classes themselves related? We consider the problem of moving from less to more computationally capable classes in the search for finite descriptions of unpredictable data series.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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. J. P. Crutchfield and K. Young. Inferring statistical complexity. Phys. Rev. Lett. 63, 105 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  2. C. E. Shannon and W. Weaver. The Mathematical Theory of Communication. University of Illinois Press, Champaign-Urbana, 1962.

    Google Scholar 

  3. A. N. Kolmogorov and V. M. Tikhomirov. e-entropy and e-capacity of sets in function spaces. Usp. Math. Nauk. 14, 3 (1959) (Math. Rev. 22, No. 2890).

    MATH  Google Scholar 

  4. R. J. Solomonof A formal theory of inductive control. Info. Control 7, 224 (1964).

    Article  Google Scholar 

  5. A. N. Kolmogorov. Three approaches to the concept of the amount of information. Prob. Info. Trans. 1, 1 (1965).

    Google Scholar 

  6. G. Chaitin. On the length of programs for computing finite binary sequences. J. ACM 13, 145 (1966).

    Article  MathSciNet  Google Scholar 

  7. J. G. Kemeny. The use of simplicity in induction. Phil. Rev. 62, 391 (1953).

    Article  Google Scholar 

  8. E. T. Jaynes. Where do we stand on maximum entropy? In Essays on Probability, Statistics, and Statistical Physics. Ed. E. T. Jaynes. Reidel, London, 1983, p. 210.

    Google Scholar 

  9. J. Rissanen. Stochastic complexity and modeling. Ann. Statistics 14, 1080 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  10. J. P. Crutchfield and B. S. McNamara. Equations of motion from a data series. Complex Systems 1, 417 (1987).

    MathSciNet  MATH  Google Scholar 

  11. D. Angluin and C. H. Smith. Inductive inference: theory and methods. Comp. Surveys 15, 237 (1983).

    Article  MathSciNet  Google Scholar 

  12. J. P. Crutchfield and N. H. Packard.: Symbolic dynamics of one-dimensional maps Entropies, finite precision, and noise. Int. J. Theor. Phys. 21, 433 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. P. Crutchfield. Noisy chaos. PhD Thesis, University of California, Santa Cruz. Published by University Microfilms Intl., Minnesota, 1983.

    Google Scholar 

  14. R. E. Blahut. Principles and Practice of Information Theory. Addision-Wesley, Reading, 1987.

    MATH  Google Scholar 

  15. A. Renyi. On the dimension and entropy of probability distributions. Acta Math. Hung. 10, 193 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  16. D. M. Cvetkovic, M. Doob and H. Sachs. Spectra of Graphs. Academic Press, New York, 1980.

    Google Scholar 

  17. R. Fischer. Sofie systems and graphs. Monatsh. Math. 80, 179 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  18. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, 1979.

    MATH  Google Scholar 

  19. N. Chomsky. Three models for the description of language. IRE Trans. Info. Th. 2, 113 (1956).

    Article  MATH  Google Scholar 

  20. J. P. Crutchfield and K. Young. Finitary ?-machines. In preparation, 1989.

    Google Scholar 

  21. J. P. Crutchfield and K. Young. Computation at the onset of chaos. In Entropy, Complexity, and the Physics of Information. Ed. W. Zurek. Addison-Wesley, Reading, 1990.

    Google Scholar 

  22. J. P. Crutchfield and E. Friedman. Language cascades: A universal structure at the onset of chaos. Preprint, 1990.

    Google Scholar 

  23. D. Huffman. The synthesis of sequential switching circuits. J. Franklin Inst. 257, 161, 275 (1954).

    Article  MathSciNet  Google Scholar 

  24. J. P. Crutchfield and N. H. Packard. Noise scaling of symbolic dynamics entropies. In Evolution of Order and Chaos. Ed. H. Haken. Springer, Berlin, 1982, p. 215.

    Chapter  Google Scholar 

  25. J. P. Crutchfield and N. H. Packard. Symbolic dynamics of noisy chaos. Physica 7D, 201 (1983).

    MathSciNet  Google Scholar 

  26. P. Grassberger. Toward a quantitative theory of self-generated complexity. Int. J. Theor. Phys. 25, 907 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  27. J. P. Crutchfield. Inferring the dynamic, quantifying physical complexity. In Measures of Complexity and Chaos. Eds. N. B. Abraham, A. M. Albano, A. Pas-samante, and P. E. Rapp. Plenum, New York, 1989, p. 327.

    Chapter  Google Scholar 

  28. S. Wolfram. Computation theory of cellular automata. Commun. Math. Phys. 96, 15 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. R. Rammal, G. Toulouse, and M. A. Virasoro. Ultrametricity for physicists. Rev. Mod. Phys. 58, 765 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  30. J. P. Crutchfield. Information and its metric. In Nonlinear Structures in Physical Systems — Pattern Formation, Chaos and Waves. Eds. L. Lam and H. C. Morris, Springer, Berlin, 1989.

    Google Scholar 

  31. E. Levin, N. Tishby, and S. A. Solla. A statistical approach to learning in layered neural networks. In Computational Learning Theory. Eds. R. Rivest, D. Haussler, and M. K. Warmuth. Morgan Kaufmann, San Mateo, California, 1989, p. 245.

    Google Scholar 

  32. D. C. Dennett. The Intentional Stance. MIT Press, Cambridge, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Crutchfield, J.P. (1991). Reconstructing Language Hierarchies. In: Atmanspacher, H., Scheingraber, H. (eds) Information Dynamics. NATO ASI Series, vol 256. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2305-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-2305-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-2307-3

  • Online ISBN: 978-1-4899-2305-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics