Related papers: Using biased coins as oracles
Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as…
Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping -- when…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. For weak coin…
Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also…
Can a computer which runs for time $\omega^2$ compute more than one which runs for time $\omega$? No. Not, at least, for the infinite computer we describe. Our computer gets more powerful when the set of its steps gets larger. We prove that…
We study a problem related to coin flipping, coding theory, and noise sensitivity. Consider a source of truly random bits $x \in \bits^n$, and $k$ parties, who have noisy versions of the source bits $y^i \in \bits^n$, where for all $i$ and…
Suppose a coin with unknown probability $p$ of heads can be flipped as often as desired. A Bernoulli factory for a function $f$ is an algorithm that uses flips of the coin together with auxiliary randomness to flip a single coin with…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
This paper studies the trade-off between two different kinds of pure exploration: breadth versus depth. The most biased coin problem asks how many total coin flips are required to identify a "heavy" coin from an infinite bag containing both…
Quantum protocols for coin-flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Does combining a finite collection of objects infinitely many times guarantee the construction of a particular object? Here we use recursive function theory to examine the popular scenario of an infinite collection of typing monkeys…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…