Emanuele Viola

We study the complexity of building

pseudorandom generators (PRGs) from hard functions.

We show that, starting from a function f : {0,1}^l -> {0,1} that

is mildly hard on average, i.e. every circuit of size 2^Omega(l)

fails to compute f on at least a 1/poly(l)

fraction of inputs, we can ...
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Emanuele Viola

We study pseudorandom generator (PRG) constructions $G^f : {0,1}^l \to {0,1}^{l+s}$ from one-way functions $f : {0,1}^n \to {0,1}^m$. We consider PRG constructions of the form $G^f(x) = C(f(q_{1}) \ldots f(q_{poly(n)}))$

where $C$ is a polynomial-size constant depth circuit

and $C$ and the $q$'s are generated from $x$ arbitrarily.

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Dean Doron, Raghu Meka, Omer Reingold, Avishay Tal, Salil Vadhan

We study monotone branching programs, wherein the states at each time step can be ordered so that edges with the same labels never cross each other. Equivalently, for each fixed input, the transition functions are a monotone function of the state.

We prove that constant-width monotone branching programs of ... more >>>

Mrinal Kumar, Varun Ramanathan, Ramprasad Saptharishi

For every constant $d$, we design a subexponential time deterministic algorithm that takes as input a multivariate polynomial $f$ given as a constant depth algebraic circuit over the field of rational numbers, and outputs all irreducible factors of $f$ of degree at most $d$ together with their respective multiplicities. Moreover, ... more >>>