Typically-Correct Derandomization for Small Time and Space

Author William M. Hoza

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William M. Hoza
  • Department of Computer Science, University of Texas at Austin, USA


We thank Michael Forbes, Scott Aaronson, David Zuckerman, Adam Klivans, and Anna Gál for helpful comments on an early draft of this paper. We thank Amnon Ta-Shma, Lijie Chen, Chris Umans, David Zuckerman, Adam Klivans, Anna Gál, Gil Cohen, Shachar Lovett, Oded Goldreich, and Avi Wigderson for helpful discussions.

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William M. Hoza. Typically-Correct Derandomization for Small Time and Space. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 9:1-9:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Probabilistic computation
  • Theory of computation → Complexity classes
  • Derandomization
  • pseudorandomness
  • space complexity


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