Related papers: Algorithmic Permutation of part of the Torah
An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the…
Technology has increasingly become an integral part of the Bible translation process. Over time, both the translation process and relevant technology have evolved greatly. More recently, the field of Natural Language Processing (NLP) has…
This paper introduces sweeping permutation automata, which move over an input string in alternating left-to-right and right-to-left sweeps and have a bijective transition function. It is proved that these automata recognize the same family…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
A refinement of Shor's Algorithm for determining order is introduced, which determines a divisor of the order after any one run of a quantum computer with almost absolute certainty. The information garnered from each run is accumulated to…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
This study is an attempt to build a contemporary linguistic corpus for Arabic language. The corpus produced, is a text corpus includes more than five million newspaper articles. It contains over a billion and a half words in total, out of…
Two groups are said to have the same character table if a permutation of the rows and a permutation of the columns of one table produces the other table. The problem of determining when two groups have the same character table is…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
We first study birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of $ 3 \times 3 $ matrices. We introduce a semi-numerical analysis which enables to compute the Arnold complexities…
In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…
A unit fraction representation of a rational number $r$ is a finite sum of reciprocals of positive integers that equals $r$. Of particular interest is the case when all denominators in the representation are distinct, resulting in an…
A reformulation of the path length of binary search trees is given in terms of permutations, allowing to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with…
Most existing models for multilingual natural language processing (NLP) treat language as a discrete category, and make predictions for either one language or the other. In contrast, we propose using continuous vector representations of…
The first step in any NLP pipeline is to split the text into individual tokens. The most obvious and straightforward approach is to use words as tokens. However, given a large text corpus, representing all the words is not efficient in…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
To mine large digital libraries in humanistically meaningful ways, scholars need to divide them by genre. This is a task that classification algorithms are well suited to assist, but they need adjustment to address the specific challenges…
Arabic is one of the languages that present special challenges to Optical character recognition (OCR). The main challenge in Arabic is that it is mostly cursive. Therefore, a segmentation process must be carried out to determine where the…