Pseudorandom generators in propositional proof complexity

Authors:
M. Alekhnovich;E. Ben-Sasson;A. A. Razborov;A. Wigderson
Affiliations:
-;-;-;-
Venue:
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Year:
2000

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Abstract

We call a pseudorandom generator G/sub n/:{0,1}/sup n//spl rarr/{0,1}/sup m/ hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement G/sub n/(x/sub 1/,...,x/sub n/)/spl ne/b for any string b/spl epsiv/{0,1}/sup m/. We consider a variety of "combinatorial" pseudorandom generators inspired by the Nisan-Wigderson generator on 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).