TY - GEN
T1 - Exponential lower bounds for AC0-frege imply superpolynomial frege lower bounds
AU - Filmus, Yuval
AU - Pitassi, Toniann
AU - Santhanam, Rahul
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79959987175&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22006-7_52
DO - 10.1007/978-3-642-22006-7_52
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AN - SCOPUS:79959987175
SN - 9783642220050
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 618
EP - 629
BT - Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
T2 - 38th International Colloquium on Automata, Languages and Programming, ICALP 2011
Y2 - 4 July 2011 through 8 July 2011
ER -