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 - http://www.scopus.com/inward/record.url?scp=0034497113&partnerID=8YFLogxK
U2 - 10.1109/SFCS.2000.892064
DO - 10.1109/SFCS.2000.892064
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AN - SCOPUS:0034497113
SN - 0272-5428
SP - 43
EP - 53
JO - Annual Symposium on Foundations of Computer Science - Proceedings
JF - Annual Symposium on Foundations of Computer Science - Proceedings
ER -