Algorithmic Randomness and Complexity (Theory and Applications of Computability) [Hardcover]

Rodney G. Downey (Author), Denis R. Hirschfeldt (Author)

Book Description

ISBN-10: 0387955674 | ISBN-13: 978-0387955674 | Publication Date: November 5, 2010 | Edition: 1st Edition.

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Editorial Reviews

From the Back Cover

Intuitively, a sequence such as 101010101010101010… does not seem random, whereas 101101011101010100…, obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by Martin-Löf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a reference tool for experts and a guide for newcomers. It surveys a broad section of work in the area, and presents most of its major results and techniques in depth. Its organization is designed to guide the reader through this large body of work, providing context for its many concepts and theorems, discussing their significance, and highlighting their interactions. It includes a discussion of effective dimension, which allows us to assign concepts like Hausdorff dimension to individual reals, and a focused but detailed introduction to computability theory. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science.

Product Details

• Hardcover: 883 pages
• Publisher: Springer; 1st Edition. edition (November 5, 2010)
• Language: English
• ISBN-10: 0387955674
• ISBN-13: 978-0387955674
• Product Dimensions: 9.4 x 6.4 x 2.3 inches
• Shipping Weight: 3.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #236,759 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

5.0 out of 5 stars Two researchers in love with their field release this long-awaited book, June 4, 2011

By 

H. Zenil (Paris, France) - See all my reviews
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This review is from: Algorithmic Randomness and Complexity (Theory and Applications of Computability) (Hardcover)

This long-awaited book is an irreplaceable source of well-presented classic and new results in algorithmic randomness and algorithmic complexity. It should be in the shelves of every theoretical computer scientist. It is clearly the product of two researchers in love with their field. Read the full review online from the (ACM) Computing Reviews (requires a password):[...]