Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.
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"If you're interested in computability theory and computational complexity, Algorithmic Information Theory belongs on your bookshelf." AI Expert
Book Description
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.
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0 of 2 people found the following review helpful:
4.0 out of 5 stars
Good book to start learning about LISP and Artificial Intelligence.,
By Hex1a4 (Ontario, Canada) - See all my reviews
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This review is from: Algorithmic Information Theory (Cambridge Tracts in Theoretical Computer Science) (Paperback)
Pretty much what I said in the title. If you're a student wanting to learn about LISP and/or Artificial Intelligence, this book is a good explanation of the fundamentals.
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First Sentence:
More than half a century has passed since the famous papers GÖDEL (1931) and TURING (1937) that shed so much light on the foundations of mathematics, and that simultaneously promulgated mathematical formalisms for specifying algorithms, in one case via primitive recursive function definitions, and in the other case via Turing machines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
program size, junk variable, register machine program, register machine instructions, exponential diophantine equation, nth bit, register machines, halting probability, digit corresponding, random real number, logical vector, minimal program, right parenthesis Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Arithmetization of Register Machines, Version of Pure, Conceptual Development, The Number of S-expressions of Size, The M-expression, Consider the S-expression, Interpreter Run, Proof Consider, Complete Example of Arithmetization, Run Elapsed Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
More than half a century has passed since the famous papers GÖDEL (1931) and TURING (1937) that shed so much light on the foundations of mathematics, and that simultaneously promulgated mathematical formalisms for specifying algorithms, in one case via primitive recursive function definitions, and in the other case via Turing machines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
program size, junk variable, register machine program, register machine instructions, exponential diophantine equation, nth bit, register machines, halting probability, digit corresponding, random real number, logical vector, minimal program, right parenthesis Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Arithmetization of Register Machines, Version of Pure, Conceptual Development, The Number of S-expressions of Size, The M-expression, Consider the S-expression, Interpreter Run, Proof Consider, Complete Example of Arithmetization, Run Elapsed Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
100
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- Information, Randomness And Incompleteness: Papers On Algorithmic Information Theory (World Scientific Series in Computer Science) by Gregory J Chaitin on 9 pages
- Frontiers of Complexity: The Search for Order in a Chaotic World by Roger Highfield in Back Matter (1), Back Matter (2), and Back Matter (3)
- Mechanistic and Nonmechanistic Science by Richard L. Thompson on page 141, page 142, and Back Matter
- New Directions in the Philosophy of Mathematics by Thomas Tymoczko on page 304, Back Matter (1), and Back Matter (2)
- Exploring Randomness (Discrete Mathematics and Theoretical Computer Science) by Gregory J. Chaitin on page 27, and page 143
See all 100 books citing this book
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