The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
On the Length of Programs for Computing Finite Binary Sequences
Open accessAbstract
The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of instructions in programs. A modified form of Turing machine is studied from the same point of view. An application to the problem of defining a patternless sequence is proposed in terms of the concepts here developed.
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“In a loose sense, FunSearch attempts to find solutions that have low Kolmogorov complexity48–50 (which is the length of the shortest computer program that produces a given object as output), whereas traditional search procedures have a very different inductive bias.”
From Mathematical discoveries from program search with large language models (2024) · cites this paper as [48]
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Citations
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 the concept of a random sequence
Church, A. (1940) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1940-07154-x · Cited by 395
Research works printed but not linked: 5
- SHANON C. E., 1956, Automata Sludiea, Shagreen aNd McCarthy, Edm
- DAVIS M., 1958, New York
- NOV MIUSES R, 1921, New York, 9
- POPERR K.R., 1959, Toronto
- VON NEUMANN J., 1963, John yon Neumann, Collected Works
Cited by
Sorted by citations
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
How to construct random functions
Goldreich, O., Goldwasser, S., & Micali, S. M. (1986) · Journal of the ACM · doi:10.1145/6490.6503 · Cited by 2,108
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
Inferring statistical complexity
Crutchfield, J. P., & Young, K. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.105 · Cited by 987
A Theory of Program Size Formally Identical to Information Theory
Chaitin, G. J. (1975) · Journal of the ACM · doi:10.1145/321892.321894 · Cited by 831
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Metadata
- Authors
- Chaitin, G. J.
- Affiliations
- City College of New York (US)
- Corresponding author
- Chaitin, Gregory J.
- Venue
- Journal of the ACM
- Published
- 1966-10
- Volume
- 13
- Issue
- 4
- Pages
- 547-569
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W1969678783
- Cited by
- 913
- References
- 2
- Citations by year
- 2026: 13 · 2025: 28 · 2024: 16 · 2023: 17 · 2022: 22 · 2021: 40 · 2020: 22 · 2019: 17 · 2018: 32 · 2017: 26 · 2016: 22 · 2015: 32 · 2014: 30 · 2013: 32 · 2012: 40
- FWCI
- 3.65
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of the ACM (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › semigroups and automata theory
- Physical Sciences › Mathematics › Theoretical Computer Science › Algorithms and Data Compression
- Keywords
- program duration, Turing machines, information theory, recursive functions, program size, Kolmogorov complexity
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