Related papers: Explicit separations between randomized and determ…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
Development of many futuristic technologies, such as MANET, VANET, iThings, nano-devices, depend on efficient distributed communication protocols in multi-hop ad hoc networks. A vast majority of research in this area focus on design…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
Methods like multi-agent reinforcement learning struggle to scale with growing population size. Mean-field games (MFGs) are a game-theoretic approach that can circumvent this by finding a solution for an abstract infinite population, which…
We devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
In the coordinator model of communication with $s$ servers, given an arbitrary non-negative function $f$, we study the problem of approximating the sum $\sum_{i \in [n]}f(x_i)$ up to a $1 \pm \varepsilon$ factor. Here the vector $x \in R^n$…
There are many models of distributed computing, and no unifying mathematical framework for considering them all. One way to sidestep this issue is to start with simple communication and fault models, and use them as building blocks to…
A group of $n$ users want to run a distributed protocol $\pi$ over a network where communication occurs via private point-to-point channels. Unfortunately, an adversary, who knows $\pi$, is able to maliciously flip bits on the channels. Can…
In this second part of our two-part paper, we invoke the stochastic maximum principle, conditional Hamiltonian and the coupled backward-forward stochastic differential equations of the first part [1] to derive team optimal decentralized…
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-Loef randomness and computable randomness. The latter…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as…
We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary.…
Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…
Network decomposition is a central tool in distributed graph algorithms. We present two improvements on the state of the art for network decomposition, which thus lead to improvements in the (deterministic and randomized) complexity of…
We study the problem of {\em impartial selection}, a topic that lies at the intersection of computational social choice and mechanism design. The goal is to select the most popular individual among a set of community members. The input can…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We give an exponential separation between one-way quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of Bar-Yossef et al.) Earlier such an exponential separation…
Quantum mechanics postulates random outcomes. However, a model making the same output predictions but in a deterministic manner would be, in principle, experimentally indistinguishable from quantum theory. In this work we consider such…