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Pseudorandom Generators in Propositional Proof Complexity

Summary: Pseudorandom Generators in Propositional
Proof Complexity
Michael Alekhnovich \Lambda , Eli Ben­Sasson y
Alexander A. Razborov z , Avi Wigderson x
May 11, 2000
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


Source: Alekhnovich, Michael - Institute for Advanced Study, Princeton University
Ben-Sasson, Eli - Department of Computer Science, Technion, Israel Institute of Technology


Collections: Computer Technologies and Information Sciences; Mathematics