TY - JOUR
T1 - Pseudorandom generators in propositional proof complexity
AU - Alekhnovich, Michael
AU - Ben-Sasson, Eli
AU - Razborov, Alexander A.
AU - Wigderson, Avi
PY - 2005
Y1 - 2005
N2 - We call a pseudorandom generator G n: {0,1} n → {0, 1} m hard for a propositional proof system P if P cannot efficiently prove the (properly encoded) statement G n(x 1,..., x n) ≠ b for any string b ε {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 G n: {0,1} n → {0, 1} m hard for a propositional proof system P if P cannot efficiently prove the (properly encoded) statement G n(x 1,..., x n) ≠ b for any string b ε {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).
KW - Generator
KW - Polynomial calculus
KW - Prepositional proof complexity
KW - Resolution
UR - http://www.scopus.com/inward/record.url?scp=16244379215&partnerID=8YFLogxK
U2 - 10.1137/S0097539701389944
DO - 10.1137/S0097539701389944
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AN - SCOPUS:16244379215
SN - 0097-5397
VL - 34
SP - 67
EP - 88
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 1
ER -