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- Siyao Guo, Tal Malkin, Igor Carboni Oliveira, Alon Rosen
- TCC
- 2014

The study of monotonicity and negation complexity for Boolean functions has been prevalent in complexity theory as well as in computational learning theory, but little attention has been given to it in the cryptographic context. Recently, Goldreich and Izsak (2012) have initiated a study of whether cryptographic primitives can be monotone, and showed that… (More)

- Adam R. Klivans, Pravesh Kothari, Igor Carboni Oliveira
- Electronic Colloquium on Computational Complexity
- 2013

What we'd like: f 2 NP f / 2 P/poly such that. What we'd like: f 2 NP f / 2 P/poly such that. Explicit circuit lower bounds known for very few circuit classes. What we'd like: f 2 NP f / 2 P/poly such that. Explicit circuit lower bounds known for very few circuit classes. Even for low depth circuits of AND, OR, NOT and mod-m gates, a lower bound eluded us… (More)

- Igor Carboni Oliveira
- Electronic Colloquium on Computational Complexity
- 2013

Different techniques have been used to prove several transference theorems of the form " non-trivial algorithms for a circuit class C yield circuit lower bounds against C ". In this survey we revisit many of these results. We discuss how circuit lower bounds can be obtained from deran-domization, compression, learning, and satisfiability algorithms. We also… (More)

- Eric Blais, Clément L. Canonne, Igor Carboni Oliveira, Rocco A. Servedio, Li-Yang Tan
- APPROX-RANDOM
- 2014

Boolean functions are not that monoton(ous).

- Adam R. Klivans, Pravesh Kothari, Igor Carboni Oliveira
- 2013 IEEE Conference on Computational Complexity
- 2013

Fort now and Klivans proved the following relationship between efficient learning algorithms and circuit lower bounds: if a class of boolean circuits C contained in P/poly of Boolean is exactly learnable with membership and equivalence queries in polynomial-time, then EXP^NP is not contained in C (the class EXP^NP was subsequently improved to EXP by… (More)

- Igor Carboni Oliveira, Rahul Santhanam
- Conference on Computational Complexity
- 2014

We consider C-compression games, a hybrid model between computational and communication complexity. A C-compression game for a function f : {0, 1} n → {0, 1} is a two-party communication game, where the first party Alice knows the entire input x but is restricted to use strategies computed by C-circuits, while the second party Bob initially has no… (More)

- Ryan Williams, Nikolay Vereshchagin, +22 authors Osamu Watanabe
- 2013

- Xi Chen, Igor Carboni Oliveira, Rocco A. Servedio
- Electronic Colloquium on Computational Complexity
- 2015

Let U k,N denote the Boolean function which takes as input k strings of N bits each, representing k numbers a 2 N −1}, and outputs 1 if and only if a (1) +· · ·+a (k) ≥ 2 N. Let THR t,n denote a monotone unweighted threshold gate, i.e., the Boolean function which takes as input a single string x ∈ {0, 1} n and outputs 1 if and only if x 1 + · · · + x n ≥ t.… (More)

- Igor Carboni Oliveira, Rahul Santhanam
- Electronic Colloquium on Computational Complexity
- 2016

We prove several results giving new and stronger connections between learning theory, circuit complexity and pseudorandomness. Let C be any typical class of Boolean circuits, and C[s(n)] denote n-variable C-circuits of size ≤ s(n). We show: Learning Speedups. If C[poly(n)] admits a randomized weak learning algorithm under the uniform distribution with… (More)