An Introduction to Kolmogorov Complexity and Its Applications

By Ming Li & Paul Vitányi

An Introduction to Kolmogorov Complexity and Its Applications is the definitive text on algorithmic information theory and Kolmogorov complexity. Published by Springer, this authoritative book presents a rigorous yet accessible treatment of complexity, randomness, information, and incompressibility from a computational perspective.

Widely regarded as the standard reference in the field, the book connects Kolmogorov complexity to computer science, mathematics, probability theory, information theory, machine learning, and data compression. It is extensively used in graduate courses and cited in theoretical research worldwide.

What This Book Does

This book equips readers with the formal tools to reason about information content, algorithmic randomness, and computational complexity, providing deep insight into what it means for data to be simple, complex, or random.

Key Features

• Foundational treatment of Kolmogorov complexity
• Formal link between computation, randomness, and information
• Applications to data compression and learning theory
• Rigorous proofs with strong theoretical grounding
• Standard reference in algorithmic information theory

Who Should Use This Book?

• Graduate students in computer science and mathematics
• Researchers in theoretical computer science
• Information theory and complexity theory scholars
• Machine learning and data science researchers
• Instructors teaching algorithmic information theory

Why It’s Essential

• The definitive textbook on Kolmogorov complexity
• Balances mathematical rigor with conceptual clarity
• Provides deep theoretical insight into randomness and information
• Trusted globally in graduate education and research

The foundational reference for understanding algorithmic information and complexity.
Order today from BooksGoat and master Kolmogorov complexity.

Product Details

• ISBN-13: 9783030112974
• Authors: Ming Li; Paul Vitányi
• Publisher: Springer
• Format: Paperback
• Condition: New
• Availability: In Stock
• Price: $— (Free Shipping)

Table of Contents (Highlights)

• Preliminaries and Mathematical Foundations
• Kolmogorov Complexity and Incompressibility
• Algorithmic Randomness
• Prefix Complexity and Coding
• Applications to Information Theory
• Learning Theory and Prediction
• Resource-Bounded Complexity

FAQs

• Is this a graduate-level book?
  Yes. It is primarily intended for graduate study and research.
• Does it require strong mathematical background?
  Yes. Familiarity with algorithms, probability, and discrete mathematics is recommended.
• Is this the standard reference in the field?
  Yes. It is widely regarded as the authoritative text on Kolmogorov complexity.