The Experts below are selected from a list of 30663 Experts worldwide ranked by ideXlab platform
Mingshuai Chen - One of the best experts on this subject based on the ideXlab platform.
-
interpolant synthesis for Quadratic Polynomial inequalities and combination with euf
International Joint Conference on Automated Reasoning, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities both strict and nonstrict is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $$\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct answers in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions EUF.
-
IJCAR - Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF
Automated Reasoning, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities both strict and nonstrict is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $$\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct answers in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions EUF.
-
Interpolation synthesis for Quadratic Polynomial inequalities and combination with EUF
arXiv: Logic in Computer Science, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $\mathcal{O}(n^3+nm))$, where $n$ is the number of variables and $m$ is the number of inequalities. Using the framework proposed by \cite{SSLMCS2008} for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions symbols (\textit{EUF}). The proposed approach is applicable to all existing abstract domains like \emph{octagon}, \emph{polyhedra}, \emph{ellipsoid} and so on, therefore it can be used to improve the scalability of existing verification techniques for programs and hybrid systems. In addition, we also discuss how to extend our approach to formulas beyond concave Quadratic Polynomials using Gr\"{o}bner basis.
Regilene Delazari Dos Santos Oliveira - One of the best experts on this subject based on the ideXlab platform.
-
the geometry of Quadratic Polynomial differential systems with a finite and an infinite saddle node a b
International Journal of Bifurcation and Chaos, 2014Co-Authors: Joan C Artes, Alex C Rezende, Regilene Delazari Dos Santos OliveiraAbstract:Planar Quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real Quadratic Polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artes et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincare disk. The bifurcation set of is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle.
-
global phase portraits of Quadratic Polynomial differential systems with a semi elemental triple node
International Journal of Bifurcation and Chaos, 2013Co-Authors: Joan C Artes, Alex C Rezende, Regilene Delazari Dos Santos OliveiraAbstract:Planar Quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family of all real Quadratic Polynomial differential systems which have a semi-elemental triple node (triple node with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this form. This bifurcation diagram yields 28 phase portraits for systems in counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincare disk. The bifurcation set is not only algebraic due to the presence of a surface found numerically. All points in this surface correspond to connections of separatrices.
-
the geometry of Quadratic Polynomial differential systems with a finite and an infinite saddle node a b
arXiv: Dynamical Systems, 2013Co-Authors: Joan C Artes, Alex C Rezende, Regilene Delazari Dos Santos OliveiraAbstract:The goal is to make a global study of the family QsnSN of all real Quadratic Polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give their bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of these forms. In this paper we provide the complete study of the geometry of the first two families, (A) and (B). The bifurcation diagram for the subfamily (A) yields 29 phase portraits for systems in QsnSN(A) counting phase portraits with and without limit cycles, while the bifurcation diagram for the subfamily (B) yields 16 phase portraits for systems in QsnSN(B) under the same conditions. Case (C) will yield quite more cases and will have an independent paper in short. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincar\'e disk. The bifurcation set of QsnSN(A) is not only algebraic due to the presence of a surface found numerically. All points in this surface correspond to connections of separatrices.
-
global phase portraits of Quadratic Polynomial differential systems with a semi elemental triple node
arXiv: Dynamical Systems, 2012Co-Authors: Joan C Artes, Alex C Rezende, Regilene Delazari Dos Santos OliveiraAbstract:Planar Quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem, are still open for this family. In this article we make a global study of the family QTN of all real Quadratic Polynomial differential systems which have a semi-elemental triple node (triple node with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this form. This bifurcation diagram yields 28 phase portraits for systems in QTN counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincar\'e disk. The bifurcation set is not only algebraic due to the presence of a surface found numerically. All points in this surface correspond to connections of separatrices.
-
phase portraits of Quadratic Polynomial vector fields having a rational first integral of degree 3
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Jaume Llibre, Regilene Delazari Dos Santos OliveiraAbstract:Abstract In this paper, we classify all the global phase portraits of the Quadratic Polynomial vector fields having a rational first integral of degree 3.
Michael Yampolsky - One of the best experts on this subject based on the ideXlab platform.
-
almost every real Quadratic Polynomial has a poly time computable julia set
arXiv: Dynamical Systems, 2017Co-Authors: Artem Dudko, Michael YampolskyAbstract:We prove that Collet-Eckmann rational maps have poly-time computable Julia sets. As a consequence, almost all real Quadratic Julia sets are poly-time.
-
Mating Non-Renormalizable Quadratic Polynomials
Communications in Mathematical Physics, 2008Co-Authors: Magnus Aspenberg, Michael YampolskyAbstract:In this paper we prove the existence and uniqueness of matings of the basilica with any Quadratic Polynomial which lies outside of the 1/2-limb of \({\mathcal {M}}\) , is non- renormalizable, and does not have any non-repelling periodic orbits.
Ting Gan - One of the best experts on this subject based on the ideXlab platform.
-
interpolant synthesis for Quadratic Polynomial inequalities and combination with euf
International Joint Conference on Automated Reasoning, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities both strict and nonstrict is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $$\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct answers in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions EUF.
-
IJCAR - Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF
Automated Reasoning, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities both strict and nonstrict is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $$\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct answers in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions EUF.
-
Interpolation synthesis for Quadratic Polynomial inequalities and combination with EUF
arXiv: Logic in Computer Science, 2016Co-Authors: Ting Gan, Liyun Dai, Bican Xia, Naijun Zhan, Deepak Kapur, Mingshuai ChenAbstract:An algorithm for generating interpolants for formulas which are conjunctions of Quadratic Polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that Quadratic Polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of Polynomial inequalities, using semi-definite programming in time complexity $\mathcal{O}(n^3+nm))$, where $n$ is the number of variables and $m$ is the number of inequalities. Using the framework proposed by \cite{SSLMCS2008} for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave Quadratic Polynomial inequalities and the equality theory over uninterpreted functions symbols (\textit{EUF}). The proposed approach is applicable to all existing abstract domains like \emph{octagon}, \emph{polyhedra}, \emph{ellipsoid} and so on, therefore it can be used to improve the scalability of existing verification techniques for programs and hybrid systems. In addition, we also discuss how to extend our approach to formulas beyond concave Quadratic Polynomials using Gr\"{o}bner basis.
Wenhong Wang - One of the best experts on this subject based on the ideXlab platform.
-
A Class of Quadratic Polynomial Chaotic Maps and its Application in Cryptography
IEEE Access, 2019Co-Authors: Shuqin Zhu, Congxu Zhu, Huanqing Cui, Wenhong WangAbstract:At present, the probability density of most chaotic systems is unknown, and the statistical characteristics of chaotic sequences cannot be described by the probability density of chaotic maps. This paper constructs a class of Quadratic Polynomial chaotic maps with three system parameters, which are topologically conjugated with Tent maps. The probability density functions of this kind of chaotic maps are given. Then, an arcsine function is designed to transform the chaotic sequence generated by the Quadratic Polynomial chaotic map into a new random sequence, which obeys the uniform distribution on the interval (−0.5, 0.5). In order to show the application of the new uniform random numbers, the applications of it in generating random arrangement, Gaussian measurement matrix of compressed sensing, and pseudo random number generator are discussed.