Screen LibraryInformation, randomness & incompleteness : papers on algorithmic information theory /
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on "Algorithmic Information Theory" by the author. There the s...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; Teaneck, N.J. : |
| Publication Dates: | 1987. |
| Literature type: | eBook |
| Language: | English |
| Series: |
World Scientific series in computer science ;
v. 8 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/0531#t=toc |
| Summary: |
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on "Algorithmic Information Theory" by the author. There the strongest possible version of G del's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics. |
| Carrier Form: | 1 online resource (x,272pages) . |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9789814434058 |
| Index Number: | QA267 |
| CLC: | O141 |
| Contents: | pt. I. Introductory/tutorial/survey papers. Randomness and mathematical proof, Scientific American, 1975. On the difficulty of computations, IEEE transactions on information theory, 1970. Information-theoretic computational complexity, IEEE transactions on information theory, 1974. Algorithmic information theory, encyclopedia of statistical sciences, 1982. Algorithmic information theory, IBM Journal of Research and Development, 1977 -- pt. II. Applications to metamathematics. G del's theorem and information, International Journal of Theoretical Physics, 1982. Randomness and G del's theorem, Proceedings 1985/Solvay Conference, in press. An algebraic equation for the halting probability, The Universal Turing Machine, in press. Computing the busy beaver function, Open Problems in Communication and Computation, in press -- pt. III. Applications to biology. To a mathematical definition of "life", ACM SICACT News, 1970. Toward a mathematical definition of "life", The Maximum Entropy Formalism, 1979. pt IV. Technical papers on self-delimiting programs. A theory of program size formally identical to information theory, Journal of the ACM, 1975. Incompleteness theorems for random reals, Advances in Applied Mathematics, 1987. Algorithmic entropy of sets, Computers & Mathematics with Applications, 1976. pt. V. Technical papers on blank-endmarker programs. Information-theoretic limitations of formal systems, Journal of the ACM, 1974. A note on Monte Carlo primality tests and algorithmic information theory, Communications on Pure and Applied Mathematics, 1978. Information-theoretic characterizations of recursive infinite strings, Theoretical Computer Science, 1976. Program size, oracles, and the jump operation, Osaka Journal of Mathematics, 1977 -- pt. VI. Technical papers on turing machines. On the length of programs for computing finite binary sequences, Journal of the ACM, 1966. On the length of programs for computing finite binary sequences: statistical considerations, Journal of the ACM, 1969. On the simplicity and speed of programs for computing infinite sets of natural numbers, Journal of the ACM, 1969. |