A hitting-set generator is a deterministic algorithm which generates a set of strings that intersects every dense set recognizable by a small circuit. A polynomial time hitting-set generator readily implies \(\mathcal{RP} = \mathcal{P}\). Andreev et. al. (ICALP’96, and JACM 1998) showed that if polynomial-time hitting-set generator in fact implies the much stronger conclusion \(\mathcal{BPP} = \mathcal{P}\). We simplify and improve their (and later) constructions.


Derandomization  \(\mathcal{RP}\)  \(\mathcal{BPP}\) one-sided error versus two-sided error 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Oded Goldreich
    • 1
  • Avi Wigderson
    • 2
  1. 1.Department of Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.Institute of Computer ScienceThe Hebrew University of Jerusalem Givat-RamJerusalemIsrael

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