Computational Complexity and Local Algorithms: On the Interplay Between Randomness and Computation (Lecture Notes in Computer Science #15700)

By: Oded Goldreich

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Synopsis: This volume contains a collection of studies in the areas of complexity theory and local algorithms. A common theme in most of the papers is the interplay between randomness and computation. This interplay is pivotal to some parts of complexity theory and is essential for local algorithms. The works included address a variety of topics in the areas of complexity theory and local algorithms. Within complexity theory the topics include approximation algorithms, counting problems, enumeration problems, explicit construction of expander graphs, fine grained complexity, interactive proof systems, PPT-search and pseudodeterminism, space complexity, and worst-case to average-case reductions. Within local algorithms the focus is mostly on property testing and on locally testable and decodable codes. In particular, many of the works seek to advance the study of testing graph properties in the bounded-degree graph model. Other topics in property testing include testing group properties and testing properties of affine subspaces.