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Boaz Barak works on computational complexity theory, cryptography and the mathematical foundations of machine learning. His research homepage describes these interests and identifies his textbooks and lecture notes.^[ref] His Introduction to Theoretical Computer Science by Boaz Barak develops computation through explicit models and resource bounds.

One example is pseudorandomness: a generated distribution can look random to efficient observers even though an unrestricted observer distinguishes it. Specifying the observer turns “looks random” into a mathematical guarantee, and connects a pseudorandom generator with the randomized algorithms it can safely simulate.^[ref]

Pseudorandomness means that specified tests cannot effectively distinguish a generated distribution from a genuinely random reference distribution. The allowed tests and their advantage are part of the definition. Passing a few frequency tests does not imply security against every feasible computation.

A pseudorandom generator expands a uniformly chosen $s$-bit seed to $m>s$ bits. For a test $D$, its distinguishing advantage isHere $U_k$ denotes a uniformly sampled $k$-bit string. There are at most $2^s$ generated strings, so an unrestricted test for membership in the generator's range distinguishes with advantage at least $1-2^{s-m}$. The useful claim is therefore computational indistinguishability for a restricted test class, not equality of the two distributions. Such a generator can replace random choices in an algorithm when the relevant computation is among the tests it fools.^[ref]

Silvio Micali coauthored the construction of pseudorandom function families with Oded Goldreich and Shafi Goldwasser. Their 1986 paper extends pseudorandomness from a generated binary string to a function that can be evaluated repeatedly at chosen inputs.^[ref]

A short key specifies an efficiently evaluated function even though its full truth table can be exponentially large. The comparison experiment is a single randomly chosen function, so repeated queries must receive consistent answers. That consistency distinguishes function security from supplying fresh independent random bits on every call.

Valentine Kabanets is a computer scientist whose research concerns computational complexity theory, derandomization, pseudorandomness and circuit complexity. A recurring question in his research is when efficient randomized algorithms can be replaced by efficient deterministic algorithms.^[ref]

His research description emphasizes a connection between designing fast algorithms and proving circuit lower bounds. An upper bound supplies an efficient method for a problem; a lower bound rules out methods within a specified model. In some settings, progress on one side can imply progress on the other, turning apparent obstacles into tools.^[ref]

Identity source: www2.cs.sfu.ca/~kabanets/

Venkatesan Guruswami is a computer scientist whose research includes coding theory, computational complexity theory, pseudorandomness and the complexity of approximate optimization. A major focus is list decoding of error-correcting codes.^[ref]

Ordinary unique decoding aims to recover one transmitted message; list decoding permits a bounded list of candidate messages when the received word has too many errors for uniqueness. The resulting questions connect the amount of redundancy in a error-correcting code with how much corruption can be handled efficiently. His research profile also describes work on approximate solutions to problems with NP-hardness.^[ref]

Identity source: theory.cs.berkeley.edu/

Xinyu Wu is a computer scientist whose research has included the theoretical foundations of quantum computing, pseudorandomness in quantum states and quantum channels. A 2021 Carnegie Mellon research profile describes this combination of tools from mathematics, physics and computer science.^[ref]

With Emre Yolcu and Marijn Heule, Wu also studied the complexity of proving colouring properties of Mycielski graphs. Their work connects short formal proofs with experiments on automated proof search.^[ref]