Abstract
An attempt is made to apply information-theoretic computational complexity to meta-mathematics. The paper studies the number of bits of instructions that must be given to a computer for it to perform finite and infinite tasks, and also the time 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 theorems from the axioms. © 1974, ACM. All rights reserved.
Author supplied keywords
- Gödel's incompleteness theorem
- complexity of sets
- computational complexity
- difficulty of theoremproving
- entropy of sets
- formal systems
- halting problem
- information content of axioms
- information content of sets
- information theory
- information time trade-offs
- metamathematics
- random strings
- recursive functions
- recursively enumerable sets
- size of proofs
- universal computers
Cite
CITATION STYLE
Chaitin, G. J. (1974). Information-Theoretic Limitations of Formal Systems. Journal of the ACM (JACM), 21(3), 403–424. https://doi.org/10.1145/321832.321839
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