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On the Length of Programs for Computing Finite Binary Sequences: statistical considerations
Open accessAbstract
An attempt is made to carry out a program (outlined in a previous paper) for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining a random or patternless, infinite binary sequence to be a sequence whose initial segments are all random or patternless finite binary sequences. A definition based on the bounded-transfer Turing machine is given detailed study, but insufficient understanding of this computing machine precludes a complete treatment. A computing machine is introduced which avoids these difficulties.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
On computable numbers, with an application to the entscheidungsproblem
Turing, A. M. (1937) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s2-42.1.230 · Cited by 8,283
Cited by
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
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
Computation at the edge of chaos: Phase transitions and emergent computation
Langton, C. G. (1990) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(90)90064-v · Cited by 1,527
Consistent interpretations of quantum mechanics
Omnès, R. (1992) · Reviews of Modern Physics · doi:10.1103/revmodphys.64.339 · Cited by 648
Metadata
- Authors
- Chaitin, G. J.
- Venue
- Journal of the ACM
- Published
- 1969-01
- Volume
- 16
- Issue
- 1
- Pages
- 145-159
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2154462988
- Cited by
- 918
- References
- 2
- FWCI
- 10.00
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Chaitin, G. J. (1969). On the Length of Programs for Computing Finite Binary Sequences: statistical considerations. Journal of the ACM. https://doi.org/10.1145/321495.321506
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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.
