Computational Complexity and Property Testing

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.

Inhalt

A Probabilistic Error-Correcting Scheme that Provides Partial Secrecy.- Bridging a Small Gap in the Gap Ampli cation of Assignment Testers.- On (Valiant's) Polynomial-Size Monotone Formula for Majority.- Two Comments on Targeted Canonical Derandomizers.- On the Effect of the Proximity Parameter on Property Testers.- On the Size of Depth-Three Boolean Circuits for Computing Multilinear Functions.- On the Communication Complexity Methodology for Proving Lower Bounds on the Query Complexity of Property Testing.- Super-Perfect Zero-Knowledge Proofs.- On the Relation between the Relative Earth Mover Distance and the Variation Distance (an exposition).- The Uniform Distribution is Complete with respect to Testing Identity to a Fixed Distribution.- A Note on Tolerant Testing with One-Sided Error.- On Emulating Interactive Proofs with Public Coins.- Reducing Testing Affine Spaces to Testing Linearity of Functions.- Deconstructing 1-Local Expanders.- Worst-case to Average-case Reductions for Subclasses of P.- On the Optimal Analysis of the Collision Probability Tester (an exposition).- On Constant-Depth Canonical Boolean Circuits for Computing Multilinear Functions.- Constant-Round Interactive Proof Systems for AC0[2] and NC1.- Flexible Models for Testing Graph Properties.- Pseudo-Mixing Time of Random Walks.- On Constructing Expanders for any Number of Vertices.