Academic Journal
AC^0[p] Lower Bounds Against MCSP via the Coin Problem
| العنوان: | AC^0[p] Lower Bounds Against MCSP via the Coin Problem |
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| المؤلفون: | Golovnev, Alexander, Ilango, Rahul, Impagliazzo, Russell, Kabanets, Valentine, Kolokolova, Antonina, Tal, Avishay |
| المساهمون: | Alexander Golovnev and Rahul Ilango and Russell Impagliazzo and Valentine Kabanets and Antonina Kolokolova and Avishay Tal |
| بيانات النشر: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| سنة النشر: | 2019 |
| المجموعة: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| مصطلحات موضوعية: | Minimum Circuit Size Problem (MCSP), circuit lower bounds, AC0[p], coin problem, hybrid argument, MKTP, biased random boolean functions |
| الوصف: | Minimum Circuit Size Problem (MCSP) asks to decide if a given truth table of an n-variate boolean function has circuit complexity less than a given parameter s. We prove that MCSP is hard for constant-depth circuits with mod p gates, for any prime p >= 2 (the circuit class AC^0[p]). Namely, we show that MCSP requires d-depth AC^0[p] circuits of size at least exp(N^{0.49/d}), where N=2^n is the size of an input truth table of an n-variate boolean function. Our circuit lower bound proof shows that MCSP can solve the coin problem: distinguish uniformly random N-bit strings from those generated using independent samples from a biased random coin which is 1 with probability 1/2+N^{-0.49}, and 0 otherwise. Solving the coin problem with such parameters is known to require exponentially large AC^0[p] circuits. Moreover, this also implies that MAJORITY is computable by a non-uniform AC^0 circuit of polynomial size that also has MCSP-oracle gates. The latter has a few other consequences for the complexity of MCSP, e.g., we get that any boolean function in NC^1 (i.e., computable by a polynomial-size formula) can also be computed by a non-uniform polynomial-size AC^0 circuit with MCSP-oracle gates. |
| نوع الوثيقة: | article in journal/newspaper conference object |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.66 |
| DOI: | 10.4230/LIPIcs.ICALP.2019.66 |
| الاتاحة: | https://doi.org/10.4230/LIPIcs.ICALP.2019.66 https://nbn-resolving.org/urn:nbn:de:0030-drops-106422 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.66 |
| Rights: | https://creativecommons.org/licenses/by/3.0/legalcode |
| رقم الانضمام: | edsbas.D0ED1436 |
| قاعدة البيانات: | BASE |
| DOI: | 10.4230/LIPIcs.ICALP.2019.66 |
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