| Autor: |
Cheraghchi, M, Grigorescu, E, Juba, B, Wimmer, K, Xie, N |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
| DOI: |
10.4230/lipics.icalp.2016.35 |
| Popis: |
AC 0 o MOD 2 circuits are AC 0 circuits augmented with a layer of parity gates just above the input layer. We study AC 0 o MOD 2 circuit lower bounds for computing the Boolean Inner Product functions. Recent works by Servedio and Viola (ECCC TR12-144) and Akavia et al. (ITCS 2014) have highlighted this problem as a frontier problem in circuit complexity that arose both as a first step towards solving natural special cases of the matrix rigidity problem and as a candidate for constructing pseudorandom generators of minimal complexity. We give the first superlinear lower bound for the Boolean Inner Product function against AC 0 o MOD 2 of depth four or greater. Specifically, we prove a superlinear lower bound for circuits of arbitrary constant depth, and an Ω(n 2 ) lower bound for the special case of depth-4 AC 0 o MOD 2 . Our proof of the depth-4 lower bound employs a new "moment-matching" inequality for bounded, nonnegative integer-valued random variables that may be of independent interest: we prove an optimal bound on the maximum difference between two discrete distributions' values at 0, given that their first d moments match. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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