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Theoretical computer science stuff

I'm currently a postdoc at UC Berkeley through the Simons Institute for the Theory of Computing. I study pseudorandomness and derandomization. More generally, I'm interested in computational complexity theory, the analysis of Boolean functions, and other topics in theoretical computer science.

A short explanation of what "derandomization" means (for curious outsiders)

Some algorithms use randomness to solve computational problems. For example, one of the best methods known for finding a large prime number is to pick a large number at random, check if it's prime, and try again if necessary.

You can think of randomness as a scarce computational resource — a type of algorithmic "fuel." Randomized algorithms are okay, but all else being equal, an algorithm that uses fewer random bits is better than an algorithm that uses more random bits, just like a faster algorithm is better than a slower algorithm, or a car that uses less gasoline is better than a car that uses more gasoline. Algorithms that don't use any randomness ("deterministic" algorithms) are best of all. For example, it would be nice to have a fast deterministic algorithm for finding large prime numbers. "Derandomization" is the art of converting randomized algorithms into deterministic algorithms.

One approach for using fewer random bits is to design pseudorandom generators, which use a small number of random bits to generate a long sequence of bits that "look random" and can often be used as a substitute for truly random bits. I'm especially interested in pseudorandom generators that are provably correct.

Video of a 10-minute overview of my research that I presented for the Simons Institute's "Meet the Fellows Welcome Event" (September 2021). Here are the slides from that presentation.

My research papers are listed below, sorted by the date they were first posted online (newest to oldest). If you have a question or comment, please send me an email! Like most researchers, I like getting emails about my work.

  1. Hitting Sets for Regular Branching Programs
    Andrej Bogdanov, William M. Hoza, Gautam Prakriya, and Edward Pyne
    Manuscript 2021
  2. Derandomizing Space-Bounded Computation via Pseudorandom Generators and their Generalizations
    William M. Hoza
    PhD dissertation 2021
  3. Better Pseudodistributions and Derandomization for Space-Bounded Computation
    William M. Hoza
    RANDOM 2021
  4. Fooling Constant-Depth Threshold Circuits
    Pooya Hatami, William M. Hoza, Avishay Tal, and Roei Tell
    FOCS 2021 (to appear)
  5. Pseudorandom Generators for Unbounded-Width Permutation Branching Programs
    William M. Hoza, Edward Pyne, and Salil Vadhan
    ITCS 2021
  6. Hitting Sets Give Two-Sided Derandomization of Small Space
    Kuan Cheng and William M. Hoza
    CCC 2020
  7. Log-Seed Pseudorandom Generators via Iterated Restrictions
    Dean Doron, Pooya Hatami, and William M. Hoza
    CCC 2020
  8. Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas
    Dean Doron, Pooya Hatami, and William M. Hoza
    CCC 2019
  9. Simple Optimal Hitting Sets for Small-Success RL
    William M. Hoza and David Zuckerman
    FOCS 2018SICOMP 2020
  10. Typically-Correct Derandomization for Small Time and Space
    William M. Hoza
    CCC 2019
  11. Quantum Communication-Query Tradeoffs
    William M. Hoza
    Manuscript 2017
  12. Universal Bell Correlations Do Not Exist
    Cole A. Graham and William M. Hoza
    PRL 2017
  13. Preserving Randomness for Adaptive Algorithms
    William M. Hoza and Adam R. Klivans
    RANDOM 2018
  14. Targeted Pseudorandom Generators, Simulation Advice Generators, and Derandomizing Logspace
    William M. Hoza and Chris Umans
    STOC 2017SICOMP 2021 (special issue for STOC 2017)
  15. The Adversarial Noise Threshold for Distributed Protocols
    William M. Hoza and Leonard Schulman
    SODA 2016

I'm grateful for all the mentorship I've received over the years, especially from David Zuckerman (my graduate advisor) and Leonard Schulman and Chris Umans (undergraduate research mentors).