Affiliation:
1. New York Univ., New York, NY
2. Univ. de Rennes, Rennes, France
Abstract
In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this data. A new feature of this algorithm is that the role of the algebraic part (the dependence on the degrees of the imput polynomials) and the combinatorial part (the dependence on the number of polynomials) are sparated. Another new feature is that the degrees of the polynomials in the equivalent quantifier-free formula that is output, are independent of the number of input polynomials. As special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields, and also for solving the existential problem in the first order theory over real closed fields, are obtained.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference38 articles.
1. ~ATIYAH M. F. AND MACONALD I.G. 1969. Introduction to Commutative Algebra. Addison-Wesley ~Reading Pa.]] ~ATIYAH M. F. AND MACONALD I.G. 1969. Introduction to Commutative Algebra. Addison-Wesley ~Reading Pa.]]
2. On the number of cells defined by a family of ~polynomials on a variety;~BASU S.;Mathematika,1996
Cited by
194 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Solving Tensor Low Cycle Rank Approximation;2023 IEEE International Conference on Big Data (BigData);2023-12-15
2. The Parameterized Complexity of Guarding Almost Convex Polygons;Discrete & Computational Geometry;2023-12-05
3. Faster real root decision algorithm for symmetric polynomials;Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation;2023-07-24
4. Further $$\exists {\mathbb {R}}$$-Complete Problems with PSD Matrix Factorizations;Foundations of Computational Mathematics;2023-06-22
5. Conic optimization-based algorithms for nonnegative matrix factorization;Optimization Methods and Software;2023-04-24