相关论文: New coins from old: computing with unknown bias
We investigate the possibility of "having someone carry out the work of executing a function for you, but without letting him learn anything about your input". Say Alice wants Bob to compute some known function f upon her input x, but wants…
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical…
Suppose Alice has a coin with heads probability $q$ and Bob has one with heads probability $p>q$. Now each of them will toss their coin $n$ times, and Alice will win iff she gets more heads than Bob does. Evidently the game favors Bob, but…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintuple $\p$ of real numbers satisfying inequations. Viewing…
One of the earliest cryptographic applications of quantum information was to create quantum digital cash that could not be counterfeited. In this paper, we describe a new type of quantum money: quantum coins, where all coins of the same…
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly…
Given a function $f$ on the vertex set of some graph $G$, a scenery, let a simple random walk run over the graph and produce a sequence of values. Is it possible to, with high probability, reconstruct the scenery $f$ from this random…
For given $p\in\lbrack1,\infty]$ and $g\in L^{p}\mathbb{(R)}$, we establish the existence and uniqueness of solutions $f\in L^{p}(\mathbb{R)}$, to the equation \[ f(x)-af(bx)=g(x), \] where $a\in\mathbb{R}$, $b\in\mathbb{R} \setminus…
For a fixed integer a>1, we suggest that the probability of nullity of the p-Fermat quotient q(p,a) is much lower than 1/p for any arbitrary large prime number p. For this we use various heuristics, justified by means of numerical…
Randomness processing in the Bernoulli factory framework provides a concrete setting in which quantum resources can outperform classical ones. We experimentally demonstrate an entanglement-assisted quantum Bernoulli factory based on…
The randomized $p$-value, (nonrandomized) mid-$p$-value and abstract randomized $p$-value have all been recommended for testing a null hypothesis whenever the test statistic has a discrete distribution. This paper provides a unifying…
We investigate the generalization of the mistake-bound model to continuous real-valued single variable functions. Let $\mathcal{F}_q$ be the class of absolutely continuous functions $f: [0, 1] \rightarrow \mathbb{R}$ with $||f'||_q \le 1$,…
We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
We investigate coin-flipping protocols for multiple parties in a quantum broadcast setting: (1) We propose and motivate a definition for quantum broadcast. Our model of quantum broadcast channel is new. (2) We discovered that quantum…