 
Summary: Pseudorandom Generators in Propositional
Proof Complexity
Michael Alekhnovich \Lambda , Eli BenSasson y
Alexander A. Razborov z , Avi Wigderson x
May 11, 2000
Abstract
We call a pseudorandom generator G n : f0; 1g n ! f0; 1g m hard for
a propositional proof system P if P can not efficiently prove the (prop
erly encoded) statement G n (x 1 ; : : : ; x n ) 6= b for any string b 2 f0; 1g m .
We consider a variety of ``combinatorial'' pseudorandom generators
inspired by the NisanWigderson 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).
\Lambda Moscow State University, Moscow, Russia mike@mccme.ru. Supported by INTAS
grant # 96753 and by the Russian Basic Research Foundation
y Institute of Computer Science, Hebrew University, Jerusalem, Israel. elli@cs.huji.ac.il.
z Steklov Mathematical Institute, Moscow, Russia razborov@genesis.mi.ras.ru. Sup
ported by INTAS grant # 96753 and by the Russian Basic Research Foundation; part of
