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A Triangular Decomposition Algorithm for Differential Polynomial Systems with Elementary Computation Complexity

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Journal of Systems Science & Complexity 2017年第2期30卷 464-483页

作者： ZHU Wei gao xiao-shan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.

关键词： Differential polynomial system regular triangular set saturated triangular set triangular decomposition.

Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

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Journal of Systems Science & Complexity 2019年第1期32卷 62-77页

作者： HU Youren gao xiao-shan KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematics University of Chinese Academy of Sciences Chinese Academy of Sciences

In this paper, a Ritt-Wu characteristic set method for Laurent partial differential polynomial systems is presented. The concept of Laurent regular differential chain is de?ned and its basic properties are proved. The authors give a partial method to decide whether a Laurent differential chain A is Laurent regular. The decision for whether A is Laurent regular is reduced to the decision of whether a univariate differential chain A1 is Laurent regular. For a univariate differential chain A1,the authors ?rst give a criterion for whether A1 is Laurent regular in terms of its generic zeros and then give partial results on deciding whether A1 is Laurent regular.

关键词： Newton polygon Laurent partial differential polynomial system Laurent regular triangular set Ritt-Wu characteristic set

Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

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Journal of Systems Science & Complexity 2022年第1期35卷 373-412页

作者： CHEN Yu-Ao gao xiao-shan Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success *** runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with *** a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of *** authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are *** leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.

关键词： Block cipher AES Boolean equation solving condition number hash function SHA3/Keccak HHL algorithm MPKC polynomial system solving quantum algorithm stream cipher Trivum

MULTIPLICITY-PRESERVING TRIANGULAR SET DECOMPOSITION OF TWO POLYNOMIALS

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Journal of Systems Science & Complexity 2014年第6期27卷 1320-1344页

作者： CHENG Jin-San gao xiao-shan Key Laboratory of Mathematics Mechanization Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.

关键词： Algebraic cycle multiplicity-preserving primitive polynomial remainder sequence trian-gular set decomposition.

TRACKING ERROR REDUCTION IN CNC MACHINING BY RESHAPING THE KINEMATIC TRAJECTORY

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Journal of Systems Science & Complexity 2013年第5期26卷 817-835页

作者： GUO Jianxin ZHANG Qiang gao xiao-shan Academy of Mathematics and Systems Science Chinese Academy of Sciences College of Information and Control Engineering China University of Petroleum(East China)

In this paper,a method of reducing the tracking error in CNC machining is *** structured neural network is used to approximate the discontinuous friction in CNC machining,which has jump points and *** the estimated nonlinear friction function,the reshaped trajectory can be computed from the desired one by solving a second order ODE such that when the reshaped trajectory is fed into the CNC controller,the output is the desired trajectory and the tracking error is eliminated in certain *** proposed reshape method is also shown to be robust with respect to certain parameters of the dynamic system.

关键词： CNC controller robustness structured neural network tracking error.

Foreword to the Special Issue

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Journal of Systems Science & Complexity 2019年第1期32卷 1-2页

作者： gao xiao-shan LI Hongbo WANG Dongming Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science University of Chinese Academy of Sciences Chinese Academy of Sciences LMIB–SKLSDE–School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Centre National de la Recherche Scientifique

On May 12,2019 we shall celebrate the centenary birthday of the late Professor Wu Wen-Tsun (1919-2017),one of the most famous and influential mathematicians in *** made foundational contributions to the field of topology and established Mathematics Mechanization as a *** devoted himself to an academic career of more than six decades with leadership and extensive activities of research and education across mathematics to computer science and artificial *** scope of his research spans from algebraic topology, differential topology,and algebraic geometry to automated reasoning,symbolic computation, and game theory,and to the history of *** early work in topology was a major breakthrough,leading to well-known and now classical results including the characteristic class and formulas named after *** the late 1970s,he pioneered the research of Mathematics Mechanization through his invention of the "Wu method",which revolutionized the field of automated reasoning.

关键词： shall celebrate centenary birthday established Mathematics

Time Optimal Feedrate Generation with Confined Tracking Error Based on Linear Programming

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Journal of Systems Science & Complexity 2015年第1期28卷 80-95页

作者： GUO Jianxin ZHANG Qiang gao xiao-shan LI Hongbo Academy of Mathematics and Systems Science Chinese Academy of Sciences College of Information and Control Engineering China University of Petroleum(East China)

In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is *** main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations,when the tracking error satisfies a second order linear ordinary differential *** on this simplification on the tracking error,the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming *** results are used to validate the methods.

关键词： CNC machining dynamics linear programming optimal control time optimal feedrate planning tracking error.

Toric Difference Variety

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Journal of Systems Science & Complexity 2017年第1期30卷 173-195页

作者： gao xiao-shan HUANG Zhang WANG Jie YUAN Chun-Ming Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of Sciences Department of Applied Mathematics Chengdu University of Technology

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization,difference coordinate rings, toric difference ideals, and group actions by difference tori. Connections between toric difference varieties and affine N[x]-semimodules are established by proving the one-to-one correspondence between irreducible invariant difference subvarieties and faces of N[x]-semimodules and the orbit-face correspondence. Finally, an algorithm is given to decide whether a binomial difference ideal represented by a Z[x]-lattice defines a toric difference variety.

关键词： Afflne N[x]-semimodule difference torus T-orbit toirc difference ideal toric differencevariety Z[x]-lattice.

Preface——Special Issue to Celebrate the 30th Anniversary of Journal of Systems Science and Complexity

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Journal of Systems Science & Complexity 2017年第1期30卷 1-3页

作者： gao xiao-shan CHEN Jie SHAO Jun WANG Shouyang Academy of Mathematics and Systems Science Chinese Academy of Sciences Key Laboratory of Intelligent Control and Design of Complex Systems Beijing Institute of Technology Department of Statistics University of Wisconsin-Madison

This special issue is dedicated to the 30th anniversary of Journal of Systems Science and Complexity(JSSC)which is under the auspices of the Institute of Systems Science,Chinese Academy of *** of Systems Science,Chinese Academy of Sciences was established in 1979 by scientists Chao-Chih Kwan,Wen-Tsun Wu,Guo-Zhi *** 1981,the Journal of Systems

关键词：系统科学复杂性杂志中国科学院序言科学研究所