相关论文: Using biased coins as oracles

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 show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective…

A divide-and-conquer cryptanalysis can often be mounted against some keystream generators composed of several (nonlinear) independent devices combined by a Boolean function. In particular, any parity-check relation derived from the periods…

The problem of creating a three-sided dice with the probability of it landing on each of its sides being equal to 1/3 has been around for many years. Various approaches have been attempted, but as different authors achieved at different…

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.

We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by first applying a reduction, then decomposing the position…

We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting…

Reversible computation is an unconventional form of computing where any executed sequence of operations can be executed in reverse at any point during computation. It has recently been attracting increasing attention in various research…

The Church-Turing thesis asserts that if a partial strings-to-strings function is effectively computable then it is computable by a Turing machine. In the 1930s, when Church and Turing worked on their versions of the thesis, there was a…

Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…

As deep learning based models are increasingly being used for information retrieval (IR), a major challenge is to ensure the availability of test collections for measuring their quality. Test collections are generated based on pooling…

We present a family of loss-tolerant quantum strong coin flipping protocols; each protocol differing in the number of qubits employed. For a single qubit we obtain a bias of 0.4, reproducing the result of Berl\'{i}n et al. [Phys. Rev. A 80,…

Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…

We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

A neat question involving coin flips surfaced on $\Bbb X$, and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at each appearance of two consecutive heads, and Bob wins a…

The brain is often called a computer and likened to a Turing machine, in part because the mind can manipulate discrete symbols such as numbers. But the brain is a dynamical system, more like a Watt governor than a Turing machine. Can a…

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…

With the current ongoing debate about fairness, explainability and transparency of machine learning models, their application in high-impact clinical decision-making systems must be scrutinized. We consider a real-life example of risk…

When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…