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A Theory of Program Size Formally Identical to Information Theory

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Gregory J. ChaitinAuthors Info & Claims

Journal of the ACM (JACM), Volume 22, Issue 3

Pages 329 - 340

https://doi.org/10.1145/321892.321894

Published: 01 July 1975 Publication History

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References

[1]

SOLOMONOFF, R.J. A formal theory of inductive inference. Inform. and Contr. 7 (1964), 1-22, 224-254.

Google Scholar

[2]

KOLMOGOROV, A.N. Three approaches to the quantitative definition of information. Problems of Inform. Transmission 1, 1 (Jam-March 1965), 1-7.

Google Scholar

[3]

CHAITX~, G.J. On the length of programs for computing finite binary sequences. J. ACM 1S, 4 (Oct. 1966), 547-569.

Crossref

Google Scholar

[4]

CHAITIN, G.J. On the length of programs for computing finite binary sequences: Statistical considerations. J. ACM I6, 1 (Jan. 1969), 145-159.

Crossref

Google Scholar

[5]

~OLMOGOROV, A.N. On the logical foundations of information theory and probability theory. Problems of Inform. Transmission 5, 3 (July-Sept. 1969), 1-4.

Google Scholar

[6]

LOVELAND, D.W. A variant of the Kolmogorov concept of complexity. Inform. and Contr. 15 (1969), 510-526.

Google Scholar

[7]

SCHNORR, C.P. Process complexity and effective random tests. J. Comput. and Syst. Scis. 7 (1973), 376-388.

Google Scholar

[8]

CHAITIN, G.J. On the difficulty of computations. 1EEE Trans. IT-16 (1970), 5-9.

Google Scholar

[9]

FEINSTEIN, A. Foundations of Information Theory. McGraw-Hill, New York, 1958.

Google Scholar

[10]

FANO, R. M. Transmission of Information. Wiley, New Nork, 1961.

Google Scholar

[11]

ABRAMSON, N. Information Theory and Coding. McGraw-Hill, New York, 1963.

Google Scholar

[12]

AsH, R. Information Theory. Wiley-Interscience, New York, 1965.

Google Scholar

[13]

W~LLIS, D.G. Computational complexity and probability constructions. J. ACM 17, 2 (April 1970), 241-259.

Crossref

Google Scholar

[14]

ZVONKIN, A. K., ANn LEVlN, L.A. The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russ. Math. Survs. 25, 6 (Nov.-Dec. 1970), 83-124.

Google Scholar

[15]

COVER, T.M. Universal gambling schemes and the complexity measures of Kolmogorov and Chaitin. Rep. No. 12, Statistics Dep., Stanford U., Stanford, Calif., 1974. Submitted to Ann. Statist.

Google Scholar

[16]

GEWIaTZ, W. L. Investigations in the theory of descriptive complexity. Ph.D. Thesis, New York University, 1974 (to be published as a Courant Institute rep.).

Crossref

Google Scholar

[17]

WEISS, B. The isomorphism problem in ergodic theory. Bull. Amer. Math. Soc. 78 (1972), 668-684.

Google Scholar

[18]

R~NYI, A. Foundations of Probability. Holden-Day, San Francisco, 1970.

Google Scholar

[19]

FINE, T .L . Theories of Probability: An Examination of Foundations. Academic Press, New York, 1973.

Google Scholar

[20]

COVER, T.M. On determining the irrationality of the mean of a random variable. Ann. Statist. 1 (1973), 862-471.

Google Scholar

[21]

CHAITIN, G .J . Information-theoretic computational complexity. IEEE Trans. IT-20 (1974), 10-15.

Google Scholar

[22]

LEvis, M. Mathematical Logic for Computer Scientists. Rep. TR-131, M.I.T. Project MAC, 1974, pp. 145-147, 153.

Crossref

Google Scholar

[23]

CHAITIN, G.J. Information-theoretic limitations of formal systems. J. ACM ~I, 3 (July 1974), 403--424.

Crossref

Google Scholar

[24]

MINSKY, M. L. Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs, N. J., 1967, pp. 54, 55, 66.

Crossref

Google Scholar

[25]

MINSK~, M., AND PAPERT, S. Perceptrons: An Introduction to Computational Geometry. M.I.T. Press, Cambridge, Mass., 1969, pp. 150, 153.

Crossref

Google Scholar

[26]

SCHWARTZ, J .T . On Programming: An Interim Report on the SETL Project. Installment I: Generalities. Lecture Notes, Courant Institute, New York University, New York, 1973, pp. 1-20.

Google Scholar

[27]

BENNETT, C.H. Logical reversibility of computation. IBM J. Res. Develop. 17 (1973), 525-532.

Google Scholar

[28]

DALEY, R .P . The extent and density of sequences within the minimal-program complexity hierarchies. J. Comput. and Syst. Scis. (to appear).

Crossref

Google Scholar

[29]

CHAITIN, G. J. Information-theoretic characterizations of recursive infinite strings. Submitted to Theoretical Comput. Sci.

Google Scholar

[30]

ELIAS, P. Minimum times and memories needed to compute the values of a function. J. Cornput. and Syst. Scis. (to appear).

Crossref

Google Scholar

[31]

ELIAS, P. Universal codeword sets and representations of the integers. IEEE Trans. I T (to appear).

Crossref

Google Scholar

[32]

HELLMAN, M.E. The information theoretic approach to cryptography. Center for Systems Research, Stanford U., Stanford, Calif., 1974.

Google Scholar

[33]

CHAITI~, G.J. Randomness and mathematical proof. Sc/. Amer. ~35, 5 (May 1975), in press.

Google Scholar

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Index Terms

A Theory of Program Size Formally Identical to Information Theory
1. Mathematics of computing
  1. Information theory
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation

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Published In

Journal of the ACM Volume 22, Issue 3

July 1975

133 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321892

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1975

Published in JACM Volume 22, Issue 3

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Information Foraging Theory: Adaptive Interaction with Information

A meaning based information theory - informalogical space: Basic concepts and convergence of information sequences

A theory of information need for information retrieval that connects information to knowledge

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