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Tautologies From Pseudo-Random Generators

By Jan Krajícek

Abstract

We consider tautologies formed from a pseudo-random number generator, dened in Krajcek [12] and in Alekhnovich et.al. [2]. We explain a strategy of proving their hardness for EF via a conjecture about bounded arithmetic formulated in Krajcek [12]. Further we give a purely nitary statement, in a form of a hardness condition posed on a function, equivalent to the conjecture. This is accompanied by a brief explanation, aimed at non-logicians, of the relation between propositional proof complexity and bounded arithmetic. It is a fundamental problem of mathematical logic to decide if tautologies can be inferred in propositional calculus in substantially fewer steps than it takes to check all possible truth assignments. This is closely related to the famous P/NP problem of Cook [3]. By propositional calculus I mean any text-book system based on a nite number of inference rules and axiom schemes that is sound and complete. The qualication substantially less means that the nu..

Year: 2001
OAI identifier: oai:CiteSeerX.psu:10.1.1.41.9528
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