Information-Theoretic Limitations of Formal Systems

Author:

Chaitin Gregory J.1

Affiliation:

1. Rivadavia 3580, Depto. 10A, Buenos Aires, Argentina

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Reference42 articles.

1. CHAITIN G.J. Information-theoretic aspects of Post's construction of a simple set. On the difficulty of generating all binary strings of complexity less than n. (Abstracts.) AMS Notices 19 (1972) pp. A-712 A-764. CHAITIN G.J. Information-theoretic aspects of Post's construction of a simple set. On the difficulty of generating all binary strings of complexity less than n. (Abstracts.) AMS Notices 19 (1972) pp. A-712 A-764.

2. On the greatest natural number of definitional or information complexity __<n. There are few minimal descriptions. (Abstracts.) Recursive Function Theory;CHAITIN G.J;Newsletter,1973

3. Method in the physical sciences. J. yon Neumann--Collecfed Works, Vol. VI, A. H. Taub, Ed., MacMillan;NEUMANN J;New York,1963

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