#### Filter Results:

#### Publication Year

2008

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

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)

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)

- Marcelo M Gauy, Hiê P H ` An, Igor C Oliveira
- 2014

We investigate the asymptotic version of the Erd˝ os-Ko-Rado theorem for the random k-uniform hypergraph H k (n, p). For 2 ≤ k(n) ≤ n/2, let N = n k and D = n−k k. We show that with probability tending to 1 as n → ∞, the largest intersecting subhypergraph of H k (n, p) has size (1 + o(1))p k n N , for any p n k ln 2 n k D −1. This lower bound on p is… (More)

Boolean functions are not that monoton(ous).

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)

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)

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)

We show that any depth-<i>d</i> circuit for determining whether an <i>n</i>-node graph has an <i>s</i>-to-<i>t</i> path of length at most <i>k</i> must have size <i>n</i><sup>Ω(<i>k</i><sup>1/<i>d</i></sup>/<i>d</i>)</sup> when <i>k</i>(<i>n</i>) ≤ <i>n</i><sup>1/5</sup>, and… (More)