The fastest and shortest algorithm for all well-defined problems

International Journal of Foundations of Computer Science

Volumn 13, Issue 3, 2002, Pages 431-443

  Hutter, Marcus ^a  

^a DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA   (Switzerland)

Author keywords

Acceleration; Algorithmic Information Theory; Blum's Speed up Theorem; Computational Complexity; Kolmogorov Complexity; Levin Search

Indexed keywords

EID: 1642393842     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129054102001199     Document Type: Conference Paper

References (23)

1. L. Babai, L. Fortnow, L. A. Levin, and M. Szegedy. Checking computations in polylogarithmic time. STOC: 23rd ACM Symp. on Theory of Computation, 23:21-31, 1991.
2. M. Blum. A machine-independent theory of the complexity of recursive functions. Journal of the ACM, 14(2):322-336, 1967.
3. M.Blum. On effective procedures for speeding up algorithms. Journal of the ACM, 18(2):290-305, 1971.
4. G. J. Chaitin. On the length of programs for computing finite binary sequences. Journal of the ACM, 13(4):547-569, 1966.
5. Melvin C. Fitting. First-Order Logic and Automated Theorem Proving. Graduate Texts in Computer Science. Springer-Verlag, Berlin, 2nd edition, 1996.
6. J. Hartmanis. Relations between diagonalization, proof systems, and complexity gaps. Theoretical Computer Science, 8(2):239-253, April 1979.
7. M. Hutter. New error bounds for Solomonoff prediction. Journal of Computer and System Science, in press, 1999. ftp://ftp.idsia.ch/pub/techrep/ IDSIA-ll-00.ps.gz.
8. M. Hutter. A theory of universal artificial intelligence based on algorithmic complexity. Technical report, 62 pages, 2000. http://arxiv.org/abs/ cs.AI/0004001.
9. A. N. Kolmogorov. Three approaches to the quantitative definition of information. Problems of Information and Transmission, 1(1): 1-7, 1965.
10. L. G. Kraft. A device for quantizing, grouping and coding amphtude modified pulses. Master's thesis, Cambridge, MA, 1949.
11. L. A. Levin. Universal sequential search problems. Problems of Information Transmission, 9:265-266, 1973.
12. L. A. Levin. Randomness conservation inequalities: Information and independence in mathematical theories. Information and Control, 61:15-37, 1984.
13. M. Li and P. M. B. Vitanyi. An introduction to Kolmogorov complexity and its applications. Springer, 2nd edition, 1997.
14. J. Schmidhuber. Discovering neural nets with low Kolmogorov complexity and high generalization capability. Neural Networks, 10(5):857-873, 1997.
15. J. Schmidhuber. Algorithmic theories of everything. Report IDSIA-20-00, quantph/ 0011122, IDSIA, Manno (Lugano), Switzerland, 2000.
16. J. Schmidhuber, J. Zhao, and M. Wiering. Shifting inductive bias with successstory algorithm, adaptive Levin search, and incremental self-improvement. Machine Learning, 28:105-130, 1997.
17. C. E. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27:379-423, 623-656, 1948. Shannon-Fano codes.
18. R. J. Solomonoff. A formal theory of inductive inference: Part 1 and 2 Inform. Control, 7:1-22, 224-254, 1964.
19. R. J. Solomonoff. Complexity-based induction systems: comparisons and convergence theorems. IEEE Trans. Inform. Theory, IT-24:422-432, 1978.
20. R. J. Solomonoff. Applications of algorithmic probability to artificial intelligence. In Uncertainty in Artificial Intelligence, pages 473-491. Elsevier Science Publishers, 1986.
21. V. Strassen. Gaussian ehmination is not optimal. Numerische Mathematik, 13:354-356, 1969.
22. P. M. B. Vitanyi and M. Li. Minimum description length induction, Bayesianism, and Kolmogorov complexity. IEEE Transactions on Information Theory, 46(2) :446-464, 2000.
23. A. K. Zvonkin and L. A. Levin. The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. RMS: Russian Mathematical Surveys, 25(6):83-124, 1970.