Simplified Derandomization of BPP Using a Hitting Set Generator

  • Oded Goldreich
  • Salil Vadhan
  • Avi Wigderson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6650)


A hitting-set generator is a deterministic algorithm that generates a set of strings such that this set intersects every dense set that is recognizable by a small circuit. A polynomial time hitting-set generator readily implies \(\mathcal{RP}=\mathcal{P}\), but it is not apparent what this implies for \(\mathcal{BPP}\). Nevertheless, Andreev et al. (ICALP’96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion \(\mathcal{BPP=P}\). We simplify and improve their (and later) constructions.


Derandomization RP BPP one-sided error versus two-sided error 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Oded Goldreich
  • Salil Vadhan
  • Avi Wigderson

There are no affiliations available

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