Related papers: Limits with Signed Digit Streams
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically…
We have formerly introduced Deep Random Secrecy, a new cryptologic technique capable to ensure secrecy as close as desired from perfection against unlimited passive eavesdropping opponents. We have also formerly introduced an extended…
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
Researchers are often perplexed when their machine learning algorithms are required to deal with complex number. Various strategies are commonly employed to project complex number into real number, although it is frequently sacrificing the…
We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…
In this paper, an effective method was introduced to steganography of text document in the host image. In the available steganography methods, the message has a random form. Therefore, the embedding capacity is generally low. In the…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
With the rise of machine learning, there is a great deal of interest in treating programs as data to be fed to learning algorithms. However, programs do not start off in a form that is immediately amenable to most off-the-shelf learning…
Within numerical reasoning, understanding numbers themselves is still a challenge for existing language models. Simple generalisations, such as solving 100+200 instead of 1+2, can substantially affect model performance (Sivakumar and…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging…
Vector space representations of words capture many aspects of word similarity, but such methods tend to make vector spaces in which antonyms (as well as synonyms) are close to each other. We present a new signed spectral normalized graph…
According to Kolmogorov complexity, every finite binary string is compressible to a shortest code -- its information content -- from which it is effectively recoverable. We investigate the extent to which this holds for infinite binary…
We present a generic digit serial method (DSM) to compute the digits of a real number $V$ . Bounds on these digits, and on the errors in the associated estimates of $V$ formed from these digits, are derived. To illustrate our results, we…
Although secular, handwritten signature is one of the most reliable biometric methods used by most countries. In the last ten years, the application of technology for verification of handwritten signatures has evolved strongly, including…
We investigate the problem of decoding a bar code from a signal measured with a hand-held laser-based scanner. Rather than formulating the inverse problem as one of binary image reconstruction, we instead incorporate the symbology of the…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify…