Simplified derandomization of BPP using a hitting set generator

Oded Goldreich; Salil Vadhan; Avi Wigderson

doi:10.1007/978-3-642-22670-0_8

Simplified derandomization of BPP using a hitting set generator

Oded Goldreich^*, Salil Vadhan, Avi Wigderson

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

15 Scopus citations

Abstract

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 RP = P, but it is not apparent what this implies for BPP. Nevertheless, Andreev et al. (ICALP'96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion BPP = P. We simplify and improve their (and later) constructions.

Original language	English
Title of host publication	Studies in Complexity and Cryptography
Subtitle of host publication	Miscellanea on the Interplay between Randomness and Computation
Editors	Oded Goldreich
Pages	59-67
Number of pages	9
DOIs	https://doi.org/10.1007/978-3-642-22670-0_8
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6650 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

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

Access to Document

10.1007/978-3-642-22670-0_8

Cite this

Goldreich, O., Vadhan, S., & Wigderson, A. (2011). Simplified derandomization of BPP using a hitting set generator. In O. Goldreich (Ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation (pp. 59-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS). https://doi.org/10.1007/978-3-642-22670-0_8

Goldreich, Oded ; Vadhan, Salil ; Wigderson, Avi. / Simplified derandomization of BPP using a hitting set generator. Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. editor / Oded Goldreich. 2011. pp. 59-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Goldreich, O, Vadhan, S & Wigderson, A 2011, Simplified derandomization of BPP using a hitting set generator. in O Goldreich (ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6650 LNCS, pp. 59-67. https://doi.org/10.1007/978-3-642-22670-0_8

Simplified derandomization of BPP using a hitting set generator. / Goldreich, Oded; Vadhan, Salil; Wigderson, Avi.
Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. ed. / Oded Goldreich. 2011. p. 59-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - Vadhan, Salil

AU - Wigderson, Avi

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N2 - 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 RP = P, but it is not apparent what this implies for BPP. Nevertheless, Andreev et al. (ICALP'96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion BPP = P. We simplify and improve their (and later) constructions.

AB - 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 RP = P, but it is not apparent what this implies for BPP. Nevertheless, Andreev et al. (ICALP'96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion BPP = P. We simplify and improve their (and later) constructions.

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KW - Derandomization

KW - one-sided error versus two-sided error

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Goldreich O, Vadhan S, Wigderson A. Simplified derandomization of BPP using a hitting set generator. In Goldreich O, editor, Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. 2011. p. 59-67. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22670-0_8

Simplified derandomization of BPP using a hitting set generator

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