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An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…

Information Theory · Computer Science 2011-12-08 Michele Elia , Joachim Rosenthal , Davide Schipani

An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…

Other Computer Science · Computer Science 2014-12-04 Aleksander Reznik , Vitaly Efimov , Aleksander Soloview , Andrey Torgov

In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items…

Computer Science and Game Theory · Computer Science 2025-11-13 Argyris Deligkas , Eduard Eiben , Tiger-Lily Goldsmith , Dušan Knop , Šimon Schierreich

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…

Algebraic Geometry · Mathematics 2023-04-24 Simon Telen

We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…

Optimization and Control · Mathematics 2022-04-15 Daniel Bienstock , Alberto del Pia , Robert Hildebrand

Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…

Logic in Computer Science · Computer Science 2016-07-18 Peter Schrammel

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

Rings and Algebras · Mathematics 2013-03-21 Charles R. Johnson , Helena Šmigoc , Dian Yang

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

Numerical Analysis · Mathematics 2024-05-08 Sergio Blanes , Fernando Casas , Ander Murua

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…

Artificial Intelligence · Computer Science 2020-01-14 Vaishak Belle , Luc De Raedt

Most automated verifiers for separation logic target the symbolic-heap fragment, disallowing both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the…

Logic in Computer Science · Computer Science 2021-03-15 Jens Pagel , Florian Zuleger

Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…

Logic in Computer Science · Computer Science 2014-11-13 Wlodzimierz Drabent

We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…

Symbolic Computation · Computer Science 2016-04-05 Toshinori Oaku

Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…

Formal Languages and Automata Theory · Computer Science 2013-03-12 Lorijn van Rooijen , Marc Zeitoun

Deep learning is increasingly being used in high-stake decision making applications that affect individual lives. However, deep learning models might exhibit algorithmic discrimination behaviors with respect to protected groups, potentially…

Machine Learning · Computer Science 2020-03-20 Mengnan Du , Fan Yang , Na Zou , Xia Hu

Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-05-23 Neeraj Mittal , Vijay K. Garg

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

Formal Languages and Automata Theory · Computer Science 2013-04-26 Thomas Place , Lorijn van Rooijen , Marc Zeitoun

The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…

Numerical Analysis · Mathematics 2025-10-20 C. P. Viazminsky

Compounding is a highly productive word-formation process in some languages that is often problematic for natural language processing applications. In this paper, we investigate whether distributional semantics in the form of word…

Computation and Language · Computer Science 2015-09-16 Joachim Daiber , Lautaro Quiroz , Roger Wechsler , Stella Frank

Even though every mathematician knows intuitively what it means to "simplify" a mathematical expression, there is still no universally accepted rigorous mathematical definition of "simplify". In this paper, we shall give a simple and…

Computational Complexity · Computer Science 2019-05-22 Craig Alan Feinstein

We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…

Data Structures and Algorithms · Computer Science 2021-12-16 Pankaj K. Agarwal , Shao-Heng Ko , Kamesh Munagala , Erin Taylor
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