相关论文: Using biased coins as oracles
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those…
A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input…
We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then, we show that our protocol is optimal for a certain type of quantum…
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct…
Functioning and interaction of distributed devices and concurrent algorithms are analyzed in the context of the theory of algorithms. Our main concern here is how and under what conditions algorithmic interactive devices can be more…
We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does…
This study establishes a nontrivial upper bound on the out-of-sample $R^2$ ($R^2_{\text{OOS}}$) in return forecasting. In particular, we define a coin-flip oracle model that, under the same directional accuracy, theoretically outperforms…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant…
Penney's Ante exhibits non-transitivity when two target strings race to appear in a shared stream of coin tosses. We study instead independent string races, where each player observes their own independent and identically distributed…
In this work, we establish a nontrivial level of distribution for densities on $\{1,\ldots, N\}$ obtained by a biased coin convolution. As a consequence of sieving theory, one then derives the expected lower bound for the weight of such…
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that,…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…