Related papers: Minimum Guesswork with an Unreliable Oracle
We consider a secure source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source X and wishes to transmit this source losslessly to Bob over a rate-limited link.…
Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
In the conditional disclosure of secrets (CDS) problem, Alice and Bob (each holds an input and a common secret) wish to disclose, as efficiently as possible, the secret to Carol if and only if their inputs satisfy some function. The…
In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always)…
Two sellers compete to sell identical products to a single buyer. Each seller chooses an arbitrary mechanism, possibly involving lotteries, to sell their product. The utility-maximizing buyer can choose to participate in one or both…
In a $3$-$\mathsf{XOR}$ game $\mathcal{G}$, the verifier samples a challenge $(x,y,z)\sim \mu$ where $\mu$ is a probability distribution over $\Sigma\times\Gamma\times\Phi$, and a map $t\colon \Sigma\times\Gamma\times\Phi\to\mathcal{A}$ for…
A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…
We consider an odd-sized "jury", which votes sequentially between two states of Nature (say A and B, or Innocent and Guilty) with the majority opinion determining the verdict. Jurors have private information in the form of a signal in…
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it…
$1 - (1-x^M) ^ {2^M} > (1 - (1-x)^M) ^{2^M}$ is proved for all $x \in [0,1]$ and all $M > 1$. This confirms a conjecture about polar code, made by Wu and Siegel in 2019, that $W^{0^m 1^M}$ is more reliable than $W^{1^m 0^M}$, where $W$ is…
We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those…
There is increasing interest in learning algorithms that involve interaction between human and machine. Comparison-based queries are among the most natural ways to get feedback from humans. A challenge in designing comparison-based…
We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is…
We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, who also…
In this paper, we initiate a rigorous theoretical study of clustering with noisy queries (or a faulty oracle). Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an…
The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by…
We consider a Gaussian sequence model that contains ill-posed inverse problems as special cases. We assume that the associated operator is partially unknown in the sense that its singular functions are known and the corresponding singular…
This paper investigates the impact of perturbations on the best-response-based algorithms approximating Nash equilibria in zero-sum games, namely Double Oracle and Fictitious Play. More precisely, we assume that the oracle computing the…
This paper investigates the problem of source-channel coding for secure transmission with arbitrarily correlated side informations at both receivers. This scenario consists of an encoder (referred to as Alice) that wishes to compress a…