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Exploring RANDOMNESS / by G...
This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of program-size complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to meta-mathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic."
Monografía
monografia Rebiun36174543 https://catalogo.rebiun.org/rebiun/record/Rebiun36174543 m o d cr mnu---uuaaa 121227s2001 enk o 000 0 eng 968429439 9781447103073 electronic bk.) 1447103076 electronic bk.) 9781447110859 1447110854 1447103076 1852334177 9781852334178 10.1007/978-1-4471-0307-3 doi AU@ 000051746750 NZ1 14979074 NZ1 15315309 AU@ eng pn AU@ OCLCO GW5XE OCLCF COO OCLCQ YDX UAB OCLCQ TKN LEAUB OCLCQ INARC UKAHL OCLCO OCLCQ OCLCO OCLCL UMB bicssc COM051300 bisacsh Chaitin, Gregory J. Exploring RANDOMNESS by Gregory J. Chaitin London Springer London 2001 London London Springer London 1 online resource (x, 164 pages) 1 online resource (x, 164 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Discrete Mathematics and Theoretical Computer Science Introduction: Historical Introduction. What is LISP? Why do I like it? How to Program my Universal Turing Machine in LISP -- Program Size: A Self-Delimiting Turing Machine considered as a Set of (Program, Output) Pairs. How to Construct Self-delimiting Turing Machines: The Kraft Inequality. The Connection Between Program-Size Complexity and Algorithmic Probability. The Basic Result on Relative Complexity -- Randomness: Theoretical Interlude -- What is Randomness? My definitions. Proof that Martin-Löf Randomness is Equivalent to Martin-Löf Randomness. Proof that Solovay Randomness is Equivalent to Strong Chaitin Randomness -- Future Work: Extending AIT to the Size of Programs for Computing Infinite Sets and to Computations with Oracles. Postscript -- Letter to a Young Reader This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of program-size complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to meta-mathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic." Computer science Computer software Electronic Data Processing Software Informatique Logiciels Software Computer science Computer software Print version 9781447110859 Discrete mathematics and theoretical computer science