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We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…
We present a new way to encode weighted sums into unweighted pairwise constraints, obtaining the following results. - Define the k-SUM problem to be: given n integers in [-n^2k, n^2k] are there k which sum to zero? (It is well known that…
We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value $V_N$ of such an $N$-stage game is of the…
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key…
We analyze the sample complexity of learning graphical games from purely behavioral data. We assume that we can only observe the players' joint actions and not their payoffs. We analyze the sufficient and necessary number of samples for the…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…
The authors discuss what is provable security in cryptography. Think that provable security is asymptotic, relative, and dynamic, and only a supplement to but not a replacement of exact security analysis. Because the conjecture P != NP has…
We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update…
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions…
In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult…
We propose a quantum implementation of a capital-dependent Parrondo's paradox that uses $O(\log_2(n))$ qubits, where $n$ is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Distributed certification is a set of mechanisms that allows an all-knowing prover to convince the units of a communication network that the network's state has some desired property, such as being 3-colorable or triangle-free. Classical…
The goal of (stable) sparse recovery is to recover a $k$-sparse approximation $x*$ of a vector $x$ from linear measurements of $x$. Specifically, the goal is to recover $x*$ such that ||x-x*||_p <= C min_{k-sparse x'} ||x-x'||_q for some…
Despite the recent successes of deep neural networks in various fields such as image and speech recognition, natural language processing, and reinforcement learning, we still face big challenges in bringing the power of numeric optimization…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…