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Physics, Information, and Computation

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An Introduction to Kolmogorov Complexity and Its Applications

Part of the book series: Graduate Texts in Computer Science ((TCS))

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Abstract

Various issues in information theory and theoretical physics can be fruitfully analyzed by Kolmogorov complexity. This is the case for physical aspects of information processing and for application of complexity to physics issues. Physicists have used complexity arguments in a variety of settings like information distance, thermodynamics, chaos, biology, and philosophy. We touch briefly upon several themes, but focus on three main issues.

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History and References

  • T.M. Cover, P. Gács and R.M. Gray, Ann. Probab., 17:3(1989), 840–865.

    Article  MathSciNet  MATH  Google Scholar 

  • W.H. Zurek in [Phys. Rev. A, 40:8(1989), 4731–4751; pp. 73-89 in: Complexity, Entropy and the Physics of Information, W.H. Zurek (Ed.), Addison-Wesley, 1991; Nature, 341 (September 1989), 119-124]

    Article  MathSciNet  Google Scholar 

  • C.M. Caves in [pp. 91-115 in: Complexity, Entropy and the Physics of Information, W.H. Zurek (Ed.), Addison-Wesley, 1991; pp. 47-89 in: Physical Origins of Time Asymmetry, J.J. Halliwell, J. Perez-Mercader and W.H. Zurek, Eds., Cambridge Univ. Press, 1994].

    Google Scholar 

  • R. Schack [‘Algorithmic information and simplicity in statistical physics’, Phys. Rev. E, Submitted].

    Google Scholar 

  • J. H. Felker [Proc. IRE 40(1952), 728–729; Ibid. 42(1954), 1191].

    Article  Google Scholar 

  • J.R. Pierce. See also [J. R. Pierce and C. C. Cutler, pp. 55-109 in: F. I. Ordway, III, Ed., Advances in Space Science, Vol. 1, Academic Press, Inc., New York, 1959].

    Google Scholar 

  • [Theory of Self-Reproducing Automata, A.W. Burks, Ed., Univ. Illinois Press, Urbana, 1966].

    Google Scholar 

  • R. Landauer in [IBM J. Res. Develop., 5(1961), 183–191].

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Lecerf, Comptes Rendus, 257(1963), 2597–2600.

    MathSciNet  Google Scholar 

  • C.H. Bennett, IBM J. Res. Develop., 17(1973), 525–532.

    Article  MathSciNet  MATH  Google Scholar 

  • [C.H. Bennett, Scientific American, (Nov. 1987), 108-117.

    Google Scholar 

  • C.H. Bennett and R. Landauer, Scientific American, (July 1985), 48-56.

    Google Scholar 

  • C.H. Bennett, Int. J. Theoret. Phys., 21:12(1982), 905–940.

    Article  Google Scholar 

  • Phys. Rev. Lett., 53:12(1984), 1202-1206].

    Google Scholar 

  • [T. Toffoli, Proc. 7th Int. Colloq. Automata, Languages and Prog., Lect. Notes Comp. Sci., vol. 85, Springer-Verlag, 1980, pp. 632-644.

    Google Scholar 

  • Math. Systems Theory, 14(1981), 13-23.

    Google Scholar 

  • E. Fredkin and T. Toffoli, Int. J. Theoret. Phys., 21(1982), 219–253].

    Article  MathSciNet  MATH  Google Scholar 

  • Int. J. Theoret. Phys., 21(1982).

    Google Scholar 

  • [Proc. IEEE Workshop on Physics and Computation, Dallas, 1992 and 1994 (also: Preliminary Proceedings 1992)].

    Google Scholar 

  • C.H. Bennett [Int. J. Theoret. Phys., 21:12(1982), 905–940]

    Article  Google Scholar 

  • P.A. Benioff [Int. J. Theoret. Physics, 21(1982), 177–202.

    Article  MathSciNet  MATH  Google Scholar 

  • Ann. New York Acad. Sci., 480(1986), 475-486].

    Google Scholar 

  • R.P. Feynman [Optics News, 11(1985), 11].

    Google Scholar 

  • [C.H. Bennett, SIAM J. Comput., 18(1989), 766–776.

    Article  MathSciNet  MATH  Google Scholar 

  • R.Y. Levine and A.T. Sherman, SIAM J. Comput, 19(1990), 673–677.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Li and P.M.B. Vitányi, Proc. Royal Soc. London, Ser. A, 452(1996), 769–789].

    Article  MATH  Google Scholar 

  • [M. Li and P.M.B. Vitányi, Proc. Royal Soc. London, Ser. A, 452(1996), 769–789].

    Article  MATH  Google Scholar 

  • [C.H. Bennett, P. Gács, M. Li, P.M.B. Vitányi, and W.H. Zurek, Proc. 25th ACM Symp. Theory Comput., 1993, pp. 21-30].

    Google Scholar 

  • [R. Landauer, IBM J. Res. Develop., 5(1961), 183–191]

    Article  MathSciNet  MATH  Google Scholar 

  • [R.W. Keyes and R. Landauer, IBM J. Res. Develop., 14(1970), 152–157]

    Article  Google Scholar 

  • [C.H. Bennett, IBM J. Res. Develop., 17(1973), 525–532; BioSystems, 11(1979), 85-90.

    Article  MathSciNet  MATH  Google Scholar 

  • C.H. Bennett and R. Landauer, Scientific American, (July 1985), 48-56]

    Google Scholar 

  • [E. Fredkin and T. Toffoli, Int. J. Theoret. Phys., 21(1982), 219–253].

    Article  MathSciNet  MATH  Google Scholar 

  • [K. Likharev, Int. J. Theoret. Phys., 21(1982), 311–326].

    Article  Google Scholar 

  • [C.H. Bennett, Int. J. Theoret. Phys., 21(1982), 905–940].

    Article  Google Scholar 

  • [C.H. Bennett, IBM J. Res. Develop., 32(1988), 16–23.

    Article  MathSciNet  Google Scholar 

  • R.W. Keyes and R. Landauer. IBM J. Res. Develop., 14(1970), 152–157.

    Article  Google Scholar 

  • R. Landauer, Int. J. Theoret. Phys., 21(1982), 283; Nature, 335(October 1988), 779-784.

    Article  MATH  Google Scholar 

  • R.W. Keyes, Science, 230(October 1985), 138-144; Rev. Mod. Phys., 61(1989), 279-287.

    Google Scholar 

  • IBM J. Res. Develop., 32(1988), 24-28.

    Google Scholar 

  • Phys. Today, 45(August 1992), 42-48].

    Google Scholar 

  • [R.C. Merkle, Nanotechnology, 4(1993), 21–40].

    Article  Google Scholar 

  • [Proc. IEEE Workshop on Physics and Computation, Dallas, 1992, 227-228, 237-247, 267-270; K.E. Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation, Wiley, 1992].

    Google Scholar 

  • [M. Li and P.M.B. Vitányi, Proc. IEEE Workshop on Physics and Computation, Dallas, 1992, 42-46.

    Google Scholar 

  • C.H. Bennett, P. Gács, M. Li, P.M.B. Vitányi, and W.H. Zurek, Proc. 25th ACM Symp. Theory Comput, 1993, pp. 21-30].

    Google Scholar 

  • [M. Gell-Mann and S. Lloyd, Complexity, 2:1(1996), 44–52].

    Article  MathSciNet  Google Scholar 

  • [E. Fermi, Thermodynamics, Dover, 1956].

    Google Scholar 

  • [J. Schumacher, CWI Quarterly, 6:2(1993), 97–120].

    MathSciNet  MATH  Google Scholar 

  • C.H. Bennett, [Int. J. Theoret. Phys., 21:12(1982), 905–940; Scientific American, 255:11(1987), 108-117]

    Article  Google Scholar 

  • W.H. Zurek in [Phys. Rev. A, 40:8(1989), 4731–4751; Complexity, entropy and the physics of information, W.H. Zurek (Ed.), Addison-Wesley, 1991, pp. 73-89; Nature, 341(September 1989), 119-124]

    Article  MathSciNet  Google Scholar 

  • C.H. Bennett [Int. J. Theoret. Phys., 21:12 (1982), 905-940; Scientific American, 255:11(1987), 108–117].

    Google Scholar 

  • W.H. Zurek using “Physical entropy” arguments in [Nature, 341(September 1989), 119–124; Phys. Rev. A, 40:8(1989), 4731-4751; Complexity, entropy and the physics of information, W.H. Zurek (Ed.), Addison-Wesley, 1991, pp. 73-89].

    Article  Google Scholar 

  • [Z. Phys., 53(1929), 840-856].

    Google Scholar 

  • [H.S. Leff and A.F. Rex, Eds., Maxwell’s Demon: Entropy, Information, Computing, Princeton University Press, 1990].

    Google Scholar 

  • [R.G. Brewer and E.L. Hahn, Scientific American, December 1984, 42-49].

    Google Scholar 

  • [M. Li and P.M.B. Vitányi, Proc. 19th Int. Colloq. Automata, Languages and Prog., Lect. Notes Comp. Sci., vol. 623, Springer-Verlag, Heidelberg, 1992, 1–16].

    Google Scholar 

  • P. Gács, Proc. 2nd IEEE Workshop on Physics and Computation, 1994, 209-216.

    Google Scholar 

  • [M. Gell-Mann, The Quark and the Jaguar, W.H. Freeman, New York, 1994.

    MATH  Google Scholar 

  • M. Gell-Mann, Complexity, 1:1(1995), 16–19.

    MathSciNet  MATH  Google Scholar 

  • M. Gell-Mann and S. Lloyd, Complexity, 2:1(1996), 44–52]

    Article  MathSciNet  Google Scholar 

  • [M. Gell-Mann and J.B. Hartle, Proc. 4th Drexel Symp. Quantum Non-Intergrability—The Quantum-Classical Approach, D.H. Feng, Ed., To appear].

    Google Scholar 

  • [S. Lloyd and J.J. Slotine, Int J. Adapt. Contr. Sign. Proc, To appear].

    Google Scholar 

  • W.H. Zurek’s [Ibid.].

    Google Scholar 

  • [J. Ford, Phys. Today, (April 1983), 40-47; ‘Chaos: Solving the unsolvable, predicting the unpredictable,’ in Chaotic Dynamics and Fractals, M.F. Barnsley and S.G. Demko (Ed.), Academic Press, 1986].

    Google Scholar 

  • [R. Schack, G.M. D’Ariano, and C.M. Caves, Phys. Rev. E, 50(1994), 972]

    Article  Google Scholar 

  • R. Schack and C. Caves [Phys. Rev. E, 53:4(1996), 3257–3270; Phys. Rev. E, 53:4(1996), 3387-3401].

    Article  MathSciNet  Google Scholar 

  • [D. Ruelle, Chance and Chaos, Penguin, 1993].

    Google Scholar 

  • Zh.I. Reznikova and B. Ya. Ryabko [Problems Inform. Transmission, 22(1986), 245–249]. Francis Bacon is quoted from Sylva Sylvarum, 337, 1627.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Ming Li

  2. Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Paul Vitányi

Authors
  1. Ming Li
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  2. Paul Vitányi
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© 1997 Springer Science+Business Media New York

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Li, M., Vitányi, P. (1997). Physics, Information, and Computation. In: An Introduction to Kolmogorov Complexity and Its Applications. Graduate Texts in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2606-0_8

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  • DOI: https://doi.org/10.1007/978-1-4757-2606-0_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2608-4

  • Online ISBN: 978-1-4757-2606-0

  • eBook Packages: Springer Book Archive

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