- Published Year: 2009
- Page count: 489
- File Size: 3 MB
- Language: English
- Published by: Cambridge University Press
- Visited by: 45
- Rating/Review: 4.7
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ISBN:
9780521424264
0521424267
Keywords:
Computational complexity: A modern approach
4.7
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Introduction to 'Computational Complexity: A Modern Approach'
Welcome to the intricate world of computational complexity, where we explore the quintessential challenges and problems that define the field of computer science and mathematics. 'Computational Complexity: A Modern Approach' is a comprehensive guide, meticulously authored by Sanjeev Arora and Boaz Barak, with an aim to illuminate the depths of complexity theory. Published by Cambridge University Press, this book has become a standard reference and textbook, catering to both the novice and seasoned researchers.
Detailed Summary of the Book
The book serves as a far-reaching survey of the field, delving into foundational concepts as well as recent advancements. Spanning over 600 pages, it starts with a formal introduction to complexity theory, highlighting essential topics such as P vs NP, Boolean circuits, and the polynomial hierarchy. It systematically progresses to advanced concepts including randomness, interactive proofs, cryptographic complexity, quantum computation, and more.
Each chapter is organized to build upon previous knowledge, ensuring readers can grasp complex ideas progressively. The authors have imbued the text with an educational spirit, making it suitable for classroom use as well as independent study. Discussions are supplemented by robust exercises that challenge the reader's understanding and stimulate intellectual curiosity.
Key Takeaways
- Comprehend fundamental concepts such as NP-completeness, reducibility, and diagonalization.
- Explore the role of randomness and probabilistic algorithms in complexity.
- Gain insights into the interplay between cryptography and complexity theory.
- Investigate the implications of quantum computing within the paradigm of complexity.
- Appreciate the breadth of complexity classes beyond NP, such as co-NP, PSPACE, and BPP.
Famous Quotes from the Book
"Complexity theory seeks to answer these basic questions: What can computers do? What can they not do? And why?"
"The P vs NP problem is one of the great open problems in computer science—indeed, in all of mathematics."
Why This Book Matters
'Computational Complexity: A Modern Approach' stands as a monumental work due to its articulate and exhaustive coverage of a field that is both theoretically challenging and practically significant. The importance of the book lies in its ability to demystify complex topics, presenting them with clarity and precision that cater to a diverse audience ranging from graduate students to researchers.
The authors, both highly respected figures in theoretical computer science, bring their rich academic experience to the fore, making groundbreaking topics accessible without diluting their depth. As the forefront of complexity theory continues to evolve, this book remains an indispensable resource for those seeking to understand the limits of computation and the profound questions surrounding it.
Moreover, this work serves as a bridge connecting multiple disciplines, reflecting the interdisciplinary nature of computational complexity. It anchors abstract theoretical constructs in real-world applications, thereby underscoring its pivotal role in shaping modern technological landscapes.
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