Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation

by Oded Goldreich (editor), Itai Benjamini (Contributor), Scott Decatur (Contributor)

This volume contains a collection of studies in the areas of complexity theory and property testing. The 21 pieces of scientific work included were conducted at different times, mostly during the last decade. Although most of these works have been cited in the literature, none of them was formally published before.

Within complexity theory the topics include constant-depth Boolean circuits, explicit construction of expander graphs, interactive proof systems, monotone formulae for majority, probabilistically checkable proofs (PCPs), pseudorandomness, worst-case to average-case reductions, and zero-knowledge proofs.

Within property testing the topics include distribution testing, linearity testing, lower bounds on the query complexity (of property testing), testing graph properties, and tolerant testing. A common theme in this collection is the interplay between randomness and computation.

394 pages, Kindle Edition

Published April 3, 2020

About the author

Oded Goldreich is a professor of Computer Science at the Faculty of Mathematics and Computer Science of Weizmann Institute of Science, Israel. His research interests lie within the theory of computation and are, specifically, the interplay of randomness and computation, the foundations of cryptography, and computational complexity theory. He won the Knuth Prize in 2017.

Goldreich has contributed to the development of pseudorandomness, zero knowledge proofs, secure function evaluation, property testing, and other areas in cryptography and computational complexity.