Pseudorandom generators in propositional proof complexity

Michael Alekhnovich; Eli Ben-Sasson; Alexander A. Razborov; Avi Wigderson

doi:10.1109/SFCS.2000.892064

Pseudorandom generators in propositional proof complexity

Michael Alekhnovich
, Eli Ben-Sasson
, Alexander A. Razborov
, Avi Wigderson

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We call a pseudorandom generator G_n:(0, 1)ⁿ→(0, 1)^m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement G_n(x₁, …, x_n)≠b for any string b∈(0, 1)^m. We consider a variety of `combinatorial' pseudorandom generators inspired by the Nisan-Wigderson generator on the one hand, and by the construction of Tseitin tautologies on the other. We prove that under certain circumstances these generators are hard for such proof systems as Resolution, Polynomial Calculus and Polynomial Calculus with Resolution (PCR).

Original language	English
Pages (from-to)	43-53
Number of pages	11
Journal	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
DOIs	https://doi.org/10.1109/SFCS.2000.892064
State	Published - 2000

Access to Document

10.1109/SFCS.2000.892064

Cite this

@article{8d9a351dc89f4ed8a8ff3e07f2bdb4cf,

title = "Pseudorandom generators in propositional proof complexity",

abstract = "We call a pseudorandom generator Gn:(0, 1)n→(0, 1)m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement Gn(x1, …, xn)≠b for any string b∈(0, 1)m. We consider a variety of `combinatorial' pseudorandom generators inspired by the Nisan-Wigderson generator on the one hand, and by the construction of Tseitin tautologies on the other. We prove that under certain circumstances these generators are hard for such proof systems as Resolution, Polynomial Calculus and Polynomial Calculus with Resolution (PCR).",

author = "Michael Alekhnovich and Eli Ben-Sasson and Razborov, \{Alexander A.\} and Avi Wigderson",

year = "2000",

doi = "10.1109/SFCS.2000.892064",

language = "אנגלית",

pages = "43--53",

journal = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

issn = "0272-5428",

}

TY - JOUR

T1 - Pseudorandom generators in propositional proof complexity

AU - Alekhnovich, Michael

AU - Ben-Sasson, Eli

AU - Razborov, Alexander A.

AU - Wigderson, Avi

PY - 2000

Y1 - 2000

N2 - We call a pseudorandom generator Gn:(0, 1)n→(0, 1)m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement Gn(x1, …, xn)≠b for any string b∈(0, 1)m. We consider a variety of `combinatorial' pseudorandom generators inspired by the Nisan-Wigderson generator on the one hand, and by the construction of Tseitin tautologies on the other. We prove that under certain circumstances these generators are hard for such proof systems as Resolution, Polynomial Calculus and Polynomial Calculus with Resolution (PCR).

AB - We call a pseudorandom generator Gn:(0, 1)n→(0, 1)m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement Gn(x1, …, xn)≠b for any string b∈(0, 1)m. We consider a variety of `combinatorial' pseudorandom generators inspired by the Nisan-Wigderson generator on the one hand, and by the construction of Tseitin tautologies on the other. We prove that under certain circumstances these generators are hard for such proof systems as Resolution, Polynomial Calculus and Polynomial Calculus with Resolution (PCR).

UR - https://www.scopus.com/pages/publications/0034497113

U2 - 10.1109/SFCS.2000.892064

DO - 10.1109/SFCS.2000.892064

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0034497113

SN - 0272-5428

SP - 43

EP - 53

JO - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

JF - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

ER -

Pseudorandom generators in propositional proof complexity

Abstract

Access to Document

Other files and links

Fingerprint

Cite this