信息、随机及不完整性

内容概要

Gregory John Chaitin： (born 1947) is an Argentine-American mathematician and computer scientist.

Beginning in 2009 Chaitin has worked on metabiology, a field parallel to biology dealing with the evolution of artificial software (computer programs) instead of natural software (DNA).

Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a new incompleteness theorem in reaction to Gödel's incompleteness theorem. He attended the Bronx High School of Science and City College of New York, where he (still in his teens) developed the theories that led to his independent discovery of Kolmogorov complexity.

Chaitin has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt. Ω has the mathematical property that it is definable but not computable.

Chaitin's early work on algorithmic information theory paralleled the earlier work of Kolmogorov.

Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin's algorithm.

书籍目录

Part l--Introductory/Tutorial/Survey Papers　Randomness and mathematical proof, Scientific American, 1975　Randomness in arithmetic, Scientific American, 1988　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, 1977Part ll--Applications to Metamathematics　Godel's theorem and information, International Journal of Theoretical Physics, 1982　Randomness and Godel's theorem, Mondes en Developpement, 1986　An algebraic equation for the halting probability, The Universal Turing Machine, 1988　Computing the busy beaver function, Open Problems in Communication and Computation, 1987Part Ill--Applications to Biology　To a mathematical definition of "life", A CM SICA CT News, 1970　Toward a mathematical definition of "life", The Maximum Entropy Formalism, 1979Part IV--Technical Papers on Self-Delimiting Programs　A theory of program size formally identical to information theory, Journal of the A CM, 1975　Incompleteness theorems for random reals, Advances in Applied Mathematics, 1987　Algorithmic entropy of sets, Computers & Mathematics with Applications, 1976Part 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, 1977Part VI--Technical Papers on Turing Machines & LISP　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, 1969Part VII--Abstracts　On the length of programs for computing finite binary sequences by bounded-transfer Turing machines, AMS Notices, 1966　On the length of programs for computing finite binary sequences by bounded-transfer Turing machines II, AMS Notices, 1966　Computational complexity and G0del's incompleteness theorem, AMS Notices, 1970　Computational complexity and Godel's incompleteness theorem, A CM SIGA CT News, 1971  ..　Information-theoretic aspects of the Turing degrees, AMS Notices, 1972　Information-theoretic aspects of Post's construction of a simple set, AMS Notices, 1972　On the difficulty of generating all binary strings of complexity less than n, AMS Notices, 1972 .　On the greatest natural number of definitional or information complexity < n, Recursive Function Theory: Newsletter, 1973　A necessary and sufficient condition for an infinite binary string to be recursive, Recursive Function Theory: Newsletter, 1973　There are few minimal descriptions, Recursive Function Theory: Newsletter, 1973　Information-theoretic computational complexity, IEEE International Symposium on Information Theory, 1973　A theory of program size formally identical to information theory, IEEE International Sympo- sium on Information Theory, 1974　Recent work on algorithmic information theory, IEEE International Symposium on Information Theory, 1977Part Vlll--Bibfiography　Publications of G J Chaitin　Discussions of Chaitin's WorkEpilogue　Undecidability & randomness in pure mathematics, EUROPALIA Conference on Self-Organization, 1989　Algorithmic information & evolution, IUBS Workshop on Biological Complexity, 1988

作者简介

This book is an essential companion to Chaitin's monograph ALGORITHMIC INFORMATION THEORY and includes in easily accessible form all the main ideas of the creator and principal archi-tect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 SCIENTIFIC AMERICAN article, a transcript of a EUROPALIA 89 lecture, an essay on bi-ology, and an extensive bibliography. Its larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of Godel and Turing and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory."One will find in [Information, Randomness & Incompleteness] all kinds of "articles which are popularizations or epistemological reflections, and presentations which permit one to rapidly obtain a precise idea of the subject and of some of its applications (in particular in the biological domain).

Very complete, it is recommended to anyone who is interested in algorithmic information theory." Jean-Paul Delahaye in LA RECHERCHE "No one, but no one, is exploring to greater depths the amazing insights and theorems that flow from Godel's work on undecidability than Gregory Chaitin. His exciting discoveries and speculations in-vade such areas as logic, induction, simplicity, the philosophy of mathematics and science, random-ness, proof theory, chaos, information theory, computer complexity, diophantine nalysis, and even the origin and evolution of life." Martin Gardner "Gregory Chaitin...has proved the ultimate in undecidability theorems that the logical structure of arithmetic can be random... The assumption that the formal structure of arithmeticis precise and regular turns out to have been a time-bomb, and Chaitin has just pushed the detonator." Ian Stewart in NATURE

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