On the Length of Programs for Computing Finite Binary Sequences
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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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FunSearch attempts to find solutions that have low Kolmogorov complexity, whereas traditional search procedures have a very different inductive bias.
“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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- 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 › Computer Science › Artificial Intelligence › Algorithms and Data Compression
- Keywords
- program duration, Turing machines, information theory, recursive functions, program size, Kolmogorov complexity
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