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Abstract: An attempt is made to apply information-theoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the... (Update)
Context of citations to this paper: More
.... this information theoretic approach to metamathematics before being in possession of the notion of self delimiting programs (see [20 22] and also [53] the technical details are somewhat di#erent when programs have blanks as endmarkers. The conclusion to be drawn from...
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BibTeX entry: (Update)
Chaitin, G. J., Information-theoretic limitations of formal systems, J. ACM 21, 1974, pp. 403--424. A Note on Monte Carlo Primality Tests 9 http://citeseer.ist.psu.edu/chaitin74informationtheoretic.html More
@incollection{ chaitin87informationtheoretic,
author = "Chaitin",
title = "Information-Theoretic Limitations of Formal Systems, Journal of the {ACM}, 1974",
booktitle = "Information Randomness \& Incompleteness: Papers on Algorithmic Information Theory, Gregory J. Chaitin, World Scientific, Series in Computer Science--Vol. 8",
year = "1987",
url = "citeseer.ist.psu.edu/chaitin74informationtheoretic.html" }
Citations (may not include all citations):229 Theory of Recursive Functions and Effective Computability (context) - Rogers - 1967
200 Introduction to Mathematical Logic (context) - Mendelson - 1964
181 Mathematical Logic (context) - Shoenfield - 1967
177 Computation: Finite and Infinite Machines (context) - Minsky - 1967
65 The complexity of finite objects and the development of the .. (context) - Zvonkin, Levin - 1970
45 Recursively enumerable sets of positive integers and their d.. (context) - Post - 1965
39 Mathematical logic as based on the theory of types (context) - Russell - 1967
36 Logical basis for information theory and probability theory (context) - Kolmogorov - 1968
33 A variant of the Kolmogorov concept of complexity (context) - Loveland - 1969
32 Set Theory and the Continuum Hypothesis (context) - Cohen - 1966
31 Computability and Unsolvability (context) - Davis - 1958
30 Mathematical Logic (context) - Kleene - 1968
29 Scientific American (context) - Hawkins - 1958
27 Hilbert's tenth problem is unsolvable (context) - Davis - 1973
25 Information-theoretic computational complexity (context) - Chaitin - 1974
19 Philosophy of Mathematics and Natural Science (context) - Weyl - 1949
15 On Programming: An Interim Report on the SETL Project (context) - Schwartz - 1973
15 Computational complexity and probability constructions (context) - Willis - 1970
13 Theories of Probability---An Examination of Foundations (context) - Fine - 1973
8 Abbreviating proofs by adding new axioms (context) - Ehrenfeucht, Mycielski - 1971
7 Godel's Proof (context) - Nagel, Newman - 1959
5 On minimal-program complexity measures (context) - Loveland - 1969
4 Speed-up theorems and incompleteness theorems (context) - Arbib - 1966
4 A Profile of Mathematical Logic (context) - DeLong - 1970
4 Mathematics: Queen and Servant of Science (context) - Bell - 1951
3 the length of proofs (context) - odel, On - 1965
3 Solvable and unsolvable problems (context) - Turing - 1954
3 What is Cantor's continuum problem (context) - odel - 1964
3 the difficulty of computations - Chaitin - 1970
3 Computer studies of Turing machine problems (context) - Lin, Rado - 1965
3 Heuristic reasoning in the theory of numbers (context) - P'olya - 1959
3 Zufalligkeit und Wahrscheinlichkeit --- Eine algorithmische .. (context) - Schnorr - 1971
2 A short survey of computational complexity theory (context) - Schwartz - 1972
2 Remarks on Bertrand Russell's theory of knowledge (context) - Einstein - 1944
2 Mathematics and logic (context) - Weyl - 1946
2 the greatest natural number of definitional or information c.. (context) - Chaitin - 1973
2 Algorithms and randomness (context) - of - 1969
2 Information-theoretic aspects of Post's construction of a si.. (context) - Chaitin - 1972
1 von Neumann---Collected Works (context) - von Neumann, in - 1963
1 84--96 (context) - Quine - 1962
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.auckland.ac.nz/CDMTCS/chaitin/): More
On the Difficulty of Computations - Chaitin (1970) (Correct)
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