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We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using…
In this paper, we propose a decision procedure of reachability for linear system {\xi}' = A{\xi} + u, where the matrix A's eigenvalues can be arbitrary algebraic numbers and the input u is a vector of trigonometric-exponential polynomials.…
We study a system, called NEL, which is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented with the non-commutative self-dual connective seq. In this paper,…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…
Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
Under the Strong Exponential Time Hypothesis, an integer linear program with $n$ Boolean-valued variables and $m$ equations cannot be solved in $c^n$ time for any constant $c < 2$. If the domain of the variables is relaxed to $[0,1]$, the…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…