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Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic 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 ..."
Abstract

Cited by 45 (7 self)
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An attempt is made to apply informationtheoretic 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 theorems from the axioms.
SOME SIMPLE SIEVES
"... An ancient process for generating the sequence of prime numbers is known by the name of The Sieve of Eratosthenes. This method is presented in many textbooks and is rather widely known. However, it seems to be less widely known that, with some modifications, other interesting sequences can be genera ..."
Abstract
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An ancient process for generating the sequence of prime numbers is known by the name of The Sieve of Eratosthenes. This method is presented in many textbooks and is rather widely known. However, it seems to be less widely known that, with some modifications, other interesting sequences can be generated by essentially a sieve process. In particular,