"An Introduction to Kolmogorov Complexity and Its Applications"

Fourth Edition by M. Li and P. Vitanyi

This revised edition delves into the concept of Kolmogorov complexity (KC), a core principle in information theory that measures the information content of any object, such as a string, program, or data set. The book caters to:

• Computer scientists and mathematicians: Interested in information theory, computational complexity, and algorithmic learning theory.
• Researchers: Seeking to understand the fundamentals of KC and its diverse applications.

Key Features:

• Self-contained and Accessible: Introduces the necessary mathematical background, making it suitable for readers with varying levels of prior knowledge.
• Historical Perspective: Provides context by tracing the development of KC and highlighting key figures in the field.
• Comprehensive Coverage: Explores various aspects of KC, including:
  • Definitions and fundamental properties
  • Algorithmic randomness and related tests
  • Applications in information theory, learning theory, and computational complexity
  • Physical aspects and connections to thermodynamics
• Extensive Learning Resources: Includes:
  • Problem sets to reinforce understanding
  • Historical notes for deeper context
  • References for further exploration
  • Online solutions for selected problems (available separately)

Summary:

This comprehensive and revised edition of "An Introduction to Kolmogorov Complexity and Its Applications" serves as a valuable resource for students and researchers interested in understanding the theoretical foundation and diverse applications of KC. The book's self-contained approach, historical context, and in-depth coverage make it a valuable resource for anyone seeking to delve into this intriguing and fundamental concept of information theory.