Introduction to Property Testing

Oded Goldreich is Professor of Computer Science at the Weizmann Institute of Science and holds the Meyer W. Weisgal Professorial Chair. He has made numerous contributions to property testing and to the theory of computation at large. He is the author of several books, including the two-volume Foundations of Cryptography (Cambridge, Vol. 1 2008, Vol. 2 2009) and Computational Complexity: A Conceptual Perspective (Cambridge, 2008). He is an associate editor of the journal Computational Complexity, former editor of the Journal of Cryptology and SIAM Journal on Computing, and has been invited to speak at numerous conferences, including the 1994 International Congress of Mathematicians. Oded Goldreich was awarded the 2017 Donald E. Knuth prize for outstanding contributions to the foundation of computer science.

'The book is an authoritative source for information on property testing, having been written by an expert in the area who has been instrumental in its development … The book is laid out as a textbook, with plenty of exercises and didactic comments, and indeed it would form a good basis for a … postgraduate course on property testing … Researchers in other areas of algorithms and computational complexity theory will find the book useful as a source of concepts and techniques. It is also likely to serve as the standard reference text on property testing in the coming years.' Mark R. Jerrum, MathSciNet

• 1. The main themes; 2. Testing lineriality; 3. Low degree tests; 4. Testing monotonicity; 5. Testing dictatorships, juntas, and monomials; 6. Testing by implicit sampling; 7. Lower bounds techniques; 8. Testing graph properties in the dense graph model; 9. Testing graph properties in the bounded-degree graph model; 10. Testing graph properties in the general graph model; 11. Testing properties of distributions; 12. Ramifications and related topics; 13. Locally testable codes and proofs.