The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Randomness conservation inequalities; information and independence in mathematical theories
Open accessAbstract
The article further develops Kolmogorov's algorithmic complexity theory. The definition of randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as mutual information in individual infinite sequences. Applications to several areas, like probability theory, theory of algorithms, intuitionistic logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.
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Citations
Cites
A formal theory of inductive inference. Part II
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90131-7 · Cited by 1,758
A formal theory of inductive inference. Part I
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90223-2 · Cited by 1,192
On the Length of Programs for Computing Finite Binary Sequences
Chaitin, G. J. (1966) · Journal of the ACM · doi:10.1145/321356.321363 · Cited by 913
Cited by
How to construct random functions
Goldreich, O., Goldwasser, S., & Micali, S. (1986) · Journal of the ACM · doi:10.1145/6490.6503 · Cited by 2,115
Time/Space Trade-Offs for Reversible Computation
Bennett, C. H. (1989) · SIAM Journal on Computing · doi:10.1137/0218053 · Cited by 405
Approximation of nonlinear systems with radial basis function neural networks
Schilling, R. J., Carroll, J. J., & Al-Ajlouni, A. F. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.896792 · Cited by 263
One way functions and pseudorandom generators
Levin, L. A. (1987) · Combinatorica · doi:10.1007/bf02579323 · Cited by 257
Self-citationProbabilistic Incremental Program Evolution
Salustowicz, R., & Schmidhuber, J. (1997) · Evolutionary Computation · doi:10.1162/evco.1997.5.2.123 · Cited by 249
Metadata
- Authors
- Levin, L. A.
- Venue
- Information and Control
- Publisher
- Elsevier BV
- Published
- 1984-04
- Volume
- 61
- Issue
- 1
- Pages
- 15-37
- ISSN
- 0019-9958 (ISSN-L)
- OpenAlex
- W2041517255
- Cited by
- 256
- References
- 3
- FWCI
- 2.53
- Type
- journal article
- Language
- en
- Open access
- bronze
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
