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Pseudorandom generators in propositional proof complexity

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4 Author(s)

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 bε{0,1}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)

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Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on

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