Related papers: decimalInfinite: All Decimals In Bits, No Loss, Sa…
Binarization is an extreme network compression approach that provides large computational speedups along with energy and memory savings, albeit at significant accuracy costs. We investigate the question of where to binarize inputs at…
Existing planar map encodings neglect maps with loops. The presented scheme encodes any connected planar map in 4 bits/edge. Encoding and decoding time is O(edges). Implicit face/edge/vertex orderings and canonical encodings are discussed.
This paper first describes an `obfuscating' compiler technology developed for encrypted computing, then examines if the trivial case without encryption produces much-sought indistinguishability obfuscation.
How can an author store digital information so that it will be reliably useful, even years later when he is no longer available to answer questions? Methods that might work are not good enough; what is preserved today should be reliably…
The binary executable format is the standard method for distributing and executing software. Yet, it is also as opaque a representation of software as can be. If the binary format were augmented with metadata that provides security-relevant…
In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of…
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of…
In cryptography, encryption is the process of obscuring information to make it unreadable without special knowledge. This is usually done for secrecy, and typically for confidential communications. Encryption can also be used for…
The remarkable transmission of two bits of information via a single qubit entangled with another at the destination, is presented as an expansion of the unremarkable classical circuit that transmits the bits with two direct qubit-qubit…
We prove that every $1$-error-correcting code over a finite field can be embedded in a $1$-perfect code of some larger length. Embedding in this context means that the original code is a subcode of the resulting $1$-perfect code and can be…
Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y…
This paper devises a simple quantum bit commitment protocol that is just as easy to implement as any existing practical quantum bit commitment protocols but will be more secure. It will be infinitely close to being unconditionally fully…
Diffraction drastically limits the bit density in optical data storage. To increase the storage density, alternative strategies involving supplementary recording dimensions and robust read-out schemes must be explored. Here, we propose to…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
We present shuffle coding, a general method for optimal compression of sequences of unordered objects using bits-back coding. Data structures that can be compressed using shuffle coding include multisets, graphs, hypergraphs, and others. We…
In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
In this paper we provide a complete approach to the real numbers via decimal representations. Construction of the real numbers by Dedekind cuts, Cauchy sequences of rational numbers, and the algebraic characterization of the real number…
This work describes an example of an application of a novel method for symmetric cryptography. Its purpose is to show how a regular message can be encrypted and then decrypted in an easy, yet secure way. The encrypting method introduced in…