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Tautologies from Pseudo-Random Generators

Published online by Cambridge University Press:  15 January 2014

Jan Krajíček
Affiliation:
Mathematical Institute, Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic Institute for Theoretical Computer Science, Charles University, Prague, Czech Republic, E-mail: krajicek@matsrv.math.cas.cz
Corresponding

Abstract

We consider tautologies formed from a pseudo-random number generator, defined in Krajíček [11] and in Alekhnovich et al. [2]. We explain a strategy of proving their hardness for Extended Frege systems via a conjecture about bounded arithmetic formulated in Krajíček [11]. Further we give a purely finitary statement, in the form of a hardness condition imposed on a function, equivalent to the conjecture.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

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