相关论文: Quantifier Elimination for Normal Cone Computation…

The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite dimensions. This calculus encompasses the whole range of the standard generalized…

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…

We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

We give a quantifier elimination procedures for the extension of Presburger arithmetic with a unary threshold counting quantifier $\exists^{\ge c} y$ that determines whether the number of different $y$ satisfying some formula is at least $c…

Second quantization has been widely used in quantum mechanics and quantum chemistry, which is trivial and error-prone for researchers. Fortunately it is a good candidate for automatic evaluation with its simple, trivial and intrinsic…

We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global…

We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically…

An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…

Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems…

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…

The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of…

We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first…

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite…

The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…

We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…

Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…

This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…

We show that every finite Boolean combination of polynomial equalities and inequalities in C^n admits two uniform normal forms: an $\exists\forall$ form and a $\forall\exists$ form, each using a single polynomial equation. Both forms use…

We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the…