Related papers: An Instance-Based Algorithm for Deciding the Bias …
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
Suppose that attached to each site z in Z is a coin with bias theta(z), and only finitely many of these coins have non-zero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its…
We consider the problem of sketching the $p$-th frequency moment of a vector, $p>2$, with multiplicative error at most $1\pm \epsilon$ and \emph{with high confidence} $1-\delta$. Despite the long sequence of work on this problem, tight…
We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…
We revisit the noisy binary search model of Karp and Kleinberg, in which we have $n$ coins with unknown probabilities $p_i$ that we can flip. The coins are sorted by increasing $p_i$, and we would like to find where the probability crosses…
You play the following game: you start out with $n$ coins that all have probability $p$ to land heads. You toss all of them and you then need to set aside at least one of them, which will not be tossed again. Now you repeat the process with…
In this article we show for the first time that quantum coin flipping with security guarantees that are strictly better than any classical protocol is possible to implement with current technology. Our protocol takes into account all…
We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to…
All proper scoring rules incentivize an expert to predict \emph{accurately} (report their true estimate), but not all proper scoring rules equally incentivize \emph{precision}. Rather than treating the expert's belief as exogenously given,…
The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ``balanced'' or ``tilted'' information and that we know the number k of false…
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising…
Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit [Blu81]. Quantum information allows for protocols in the information theoretic setting where no…
Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
Is flipping a coin a deterministic process or a random one? We do not allow bounces. If we know the initial velocity and the spin given to the coin, mechanics should predict the face it lands on. However, the coin toss has been everyone's…
Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of…
Given a $p$-coin that lands heads with unknown probability $p$, we wish to produce an $f(p)$-coin for a given function $f: (0,1) \rightarrow (0,1)$. This problem is commonly known as the Bernoulli Factory and results on its solvability and…
Given a coin with unknown bias $p\in [0,1]$, can we exactly simulate another coin with bias $f(p)$? The exact set of simulable functions has been well characterized 20 years ago. In this paper, we ask the quantum counterpart of this…
The toss of a coin is usually regarded as the epitome of randomness, and has been used for ages as a means to resolve disputes in a simple, fair way. Perhaps as ancient as consulting objects such as coins and dice is the art of maliciously…