We prove that the pseudorandom generator introduced in Impagliazzo et al. (1994) fools group products of a given finite group. The seed length is $O(\log n \log 1 / \epsilon)$, where $n$ is the length of the word and $\epsilon$ is the error. The result is equivalent to the statement ... more >>>

We exhibit an explicit pseudorandom generator that stretches an $O \left( \left( w^4 \log w + \log (1/\varepsilon) \right) \cdot \log n \right)$-bit random seed to $n$ pseudorandom bits that cannot be distinguished from truly random bits by a permutation branching program of width $w$ with probability more than $\varepsilon$. ... more >>>

We show that quantum algorithms of time T and space $S \ge \log T$ with intermediate measurements can be simulated by quantum algorithms of time $T\cdot \mathrm{poly}(S)$ and space $O(S\cdot \log T)$ without intermediate measurements. The best simulations prior to this work required either $\Omega(T)$ space (by the deferred measurement ... more >>>

We study a new approach for constructing pseudorandom generators (PRGs) that fool constant-width standard-order read-once branching programs (ROBPs). Let $X$ be the $n$-bit output distribution of the INW PRG (Impagliazzo, Nisan, and Wigderson, STOC 1994), instantiated using expansion parameter $\lambda$. We prove that the bitwise XOR of $t$ independent copies ... more >>>

We construct an $\varepsilon$-error PRG for permutation read-once branching programs of length $n$ and width $w$ with seed length
$$
O\left((\log w+\log(1/\varepsilon))\cdot \log n\right).
$$
This gives an exponential improvement in the dependence on $w$ compared with the constructions of De (CCC 2011) and Steinke (ECCC 2012). Compared with the ... more >>>

Braverman, Rao, Raz, and Yehudayoff (SICOMP 2014) showed that there is an explicit pseudorandom generator (PRG) that fools standard-order regular read-once branching programs (ROBPs) with seed length
$$
O(\log n \cdot \log \log n + \log n \cdot \log(wd/\epsilon)),
$$
where $w$ is the width of ... more >>>