Exponential lower bounds for AC0-frege imply superpolynomial frege lower bounds

Yuval Filmus, Toniann Pitassi, Rahul Santhanam

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

ملخص

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.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيفAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
الصفحات618-629
عدد الصفحات12
طبعةPART 1
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2011
منشور خارجيًانعم
الحدث38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, سويسرا
المدة: ٤ يوليو ٢٠١١٨ يوليو ٢٠١١

سلسلة المنشورات

الاسمLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
الرقمPART 1
مستوى الصوت6755 LNCS

!!Conference

!!Conference38th International Colloquium on Automata, Languages and Programming, ICALP 2011
الدولة/الإقليمسويسرا
المدينةZurich
المدة٤/٠٧/١١٨/٠٧/١١

All Science Journal Classification (ASJC) codes

  • !!Theoretical Computer Science
  • !!General Computer Science

بصمة

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