Related papers: Algorithmic Permutation of part of the Torah

Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…

With the growing number of textual resources available, the ability to understand them becomes critical. An essential first step in understanding these sources is the ability to identify the part of speech in each sentence. Arabic is a…

In spite of remarkable progress in machine learning techniques, the state-of-the-art machine learning algorithms often keep machines from real-time learning (online learning) due in part to computational complexity in parameter…

Five thousand variations of the RoBERTa model, an artificially intelligent "transformer" that can understand text language, completed an English literacy exam with 29 multiple-choice questions. Data were used to calculate the psychometric…

Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck…

One of the primary tasks of morphological parsers is the disambiguation of homographs. Particularly difficult are cases of unbalanced ambiguity, where one of the possible analyses is far more frequent than the others. In such cases, there…

We train a bilingual Arabic-Hebrew language model using a transliterated version of Arabic texts in Hebrew, to ensure both languages are represented in the same script. Given the morphological, structural similarities, and the extensive…

The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…

Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…

The neural text generation suffers from the text degeneration issue such as repetition. Traditional stochastic sampling methods only focus on truncating the unreliable "tail" of the distribution, and do not address the "head" part, which we…

We consider the problem where P is an unknown permutation on {0,1,...,2^n - 1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the minimum r > 0 such that P^r(y) = y (where P^r is P composed with itself r times).…

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…

We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept…

We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…

Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…