Exponential Lower Bounds for AC0-Frege Imply Superpolynomial Frege Lower Bounds

Yuval Filmus, Toniann Pitassi, Rahul Santhanam

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

We give a general transformation which turns polynomial-size Frege proofs to subexponential-size AC0-Frege proofs. This indicates that proving exponential lower bounds for AC0-Frege is hard, since it is a longstanding open problem to prove super-polynomial lower bounds for Frege. Our construction is optimal for tree-like proofs.

As a consequence of our main result, we are able to shed some light on the question of weak automatizability for bounded-depth Frege systems. First, we present a simpler proof of the results of Bonet et al. [5] showing that under cryptographic assumptions, bounded-depth Frege proofs are not weakly automatizable. Secondly, we show that because our proof is more general, under the right cryptographic assumptions, it could resolve the weak automatizability question for lower depth Frege systems.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings, Part I
EditorsLuca Aceto, Monika Henzinger, Jiri Sgall
Place of PublicationZurich, Switzerland
Number of pages12
ISBN (Print)978-3-642-22005-0
Publication statusPublished - 1 Jul 2011

Publication series

NameLecture Notes in Computer Science


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