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

Published:11 May 2015Publication History
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Abstract

We give a general transformation that turns polynomial-size Frege proofs into subexponential-size AC0-Frege proofs. This indicates that proving truly exponential lower bounds for AC0-Frege is hard, as it is a long-standing open problem to prove superpolynomial lower bounds for Frege. Our construction is optimal for proofs of formulas of unbounded depth.

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

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 7, Issue 2
      May 2015
      101 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2775140
      Issue’s Table of Contents

      Copyright © 2015 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 11 May 2015
      • Revised: 1 October 2014
      • Accepted: 1 October 2014
      • Received: 1 January 2013
      Published in toct Volume 7, Issue 2

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