Related papers: Minimum Guesswork with an Unreliable Oracle
We study a recently introduced two-person combinatorial game, the $(a,b)$-monochromatic clique transversal game which is played by Alice and Bob on a graph $G$. As we observe, this game is equivalent to the $(b,a)$-biased Maker-Breaker game…
Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring $L$ bits of noise-free communication and make it robust over such a channel. In a…
This paper considers a two-terminal problem in which Alice and Bob aim to perform a joint measurement on a bipartite quantum system $\rho^{AB}$. Alice transmits the results of her measurements to Bob over a classical channel, and the two…
Many constructions in computability theory rely on "time tricks". In the higher setting, relativising to some oracles shows the necessity of these. We construct an oracle~$A$ and a set~$X$, higher Turing reducible to~$X$, but for which…
When allocating objects among agents with equal rights, people often evaluate the fairness of an allocation rule by comparing their received utilities to a benchmark share - a function only of her own valuation and the number of agents.…
We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used…
When fitting a particular Economic model on a sample of data, the model may turn out to be heavily misspecified for some observations. This can happen because of unmodelled idiosyncratic events, such as an abrupt but short-lived change in…
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…
We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration…
Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such pairwise…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
Identifying the top-$k$ items is fundamental but often prohibitive when exact valuations are expensive. We study a two-oracle setting with a fast, noisy weak oracle and a scarce, high-fidelity strong oracle (e.g., human expert verification…
We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied…
In this paper we consider the problem of extracting secret key from an eavesdropped source $p_{XYZ}$ at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice ($X$) and…
We study the extremal Forrelation problem, where, provided with oracle access to Boolean functions $f$ and $g$ promised to satisfy either $\textrm{forr}(f,g)=1$ or $\textrm{forr}(f,g)=-1$, one must determine (with high probability) which of…
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…
We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational…
Given two finite ordered sets $A = \{a_1, \ldots, a_m\}$ and $B = \{b_1, \ldots, b_n\}$, introduce the set of $m n$ outcomes of the game $O = \{(a, b) \mid a \in A, b \in B\} = \{(a_i, b_j) \mid i \in I = \{1, \ldots, m\}, j \in J = \{1,…