Publications of Xiao-Shan Gao

    Books

  1. S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.
  2. X.S. Gao, D.K. Wang, Z. Qiu, and H. Yang, Equation Solving and Machine Proving - Problem Solving with MMP (in Chinese ), Science Press, Beijing, 2006.
  3. X.S. Gao, J. Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese), Nine Chapters Pub., Taibei, 1998.

    Proceedings/Special Issues/Collection of Papers

  4. X.S. Gao, H. Li, D. Wang (eds.), Special Issue to Celebrate Wu Wen-Tsun＊s Centenary Birthday, Journal of Systems Science and Complexity, 32(1), 2019.
  5. X.S. Gao (editor), Algebraic and Symbolic Computation, Special Issue for ISSAC2016. Journal of Symbolic Computation, 80(3), 2017.
  6. X.S. Gao and D. Kapur (eds), Advances in Mathematics Mechanization, Journal of Symbolic Computation, 47(6), 2012.
  7. X.S. Gao, C. Hoffmann, R. Joan-Arinyo (eds), Geometric Constraints and Reasoning, CAGD, 29, 2012.
  8. X.S. Gao and D. Micheluchi (eds), Geometric Constraints, International Journal of Computational Geometry & Applications, 16, 2006.
  9. A. Cohen, X.S. Gao, N. Takayama (eds), Symbolic Computation in Algebra and Geometry, Journal of Symbolic Computation, 38, 2004.
  10. A. Cohen, X.S. Gao, N. Takayama (eds), Mathematical Software, World Scientific Pub., Singapore, 2002.
  11. X.S. Gao and D. Wang (eds), Mathematics Mechanization and Applications, Academic Press, London, 2000.
  12. X.S. Gao and D. Wang (eds), Computer Mathematics-Proc. of ASCM'2000, World Scientific, Singapore, 2000.
  13. X.S. Gao, D. Wang and L. Yang (eds), Automated Deduction in Geometry, Procs. of ADG98 Springer, Berlin, 1999.

    Research Papers

    2024

  14. Lijia Yu, Xiao-Shan Gao, Lijun Zhang. Optimal Robust Memorization with ReLU Neural Networks. ICLR 2024 (spotlight).
  15. Shuang Liu, Yihan Wang, Xiao-Shan Gao, Game-Theoretic Unlearnable Example Generator. Proceedings of the AAAI Conference on Artificial Intelligence, 38(19), 21349-21358, 2024.
  16. Yifan Zhu, Lijia Yu, Xiao-Shan Gao, Detection and Defense of Unlearnable Examples. Proceedings of the AAAI Conference on Artificial Intelligence, 38(15), 17211-17219, 2024.
  17. Yihan Wang, Shuang Liu, Xiao-Shan Gao, Data-Dependent Stability Analysis of Adversarial Training. arXiv preprint, arXiv:2401.03156.
  18. Yihan Wang, Yifan Zhu, Xiao-Shan Gao, Efficient Availability Attacks against Supervised and Contrastive Learning Simultaneously. arXiv preprint, arXiv:2402.04010.
  19. Qiao-Long Huang, Ke Ye, Xiao-Shan Gao, Skew-polynomial-sparse matrix multiplication. Journal of Symbolic Computation, 121, 2024, 102240.

    2023

  20. L. Yu, Y. Wang, and X.S. Gao, Adversarial Parameter Attack on Deep Neural Networks , ICML2023, PMLR 202:40354-40372, 2023.
  21. L. Yu and X.S. Gao, Improve the Robustness and Accuracy of Deep Neural Network with L_{2,\infty} Normalization, Journal of Systems Science and Complexity, 2023, 36(1): 3-28.
  22. Yihan Wang, Lijia Yu, and Xiao-Shian Gao. Restore Translation Using Equivariant Neural Networks, ICONIP 2023, CCIS 1962, 583-603, Springer Singapore, 2024.
  23. L. Guo, R.W. Yeung, and X.S. Gao, Proving Information Inequalities and Identities with Symbolic Computation, IEEE Transactions on Information Theory, 69(8), 4799-4811, Aug. 2023.
  24. Qin Wu, Chun-Ming Yuan, Li-Yong Shen, Shi-Tao He, Xiao-Shan Gao, Cubic time-spline fitting and interpolation for five-axis CNC machining , Journal of Computational Design and Engineering, 10(6), 2345-2360, 2023.
  25. Qiao-Long Huang and Xiao-Shan Gao, New Sparse Multivariate Polynomial Factorization Algorithms over Integers , Proc. ISSAC '23, 315每324, 2023.

    2022

  26. Xiao-Shan Gao. Mathematical Theory of Adversarial Deep Learning , Invited Talk at CSIAM 2022 Annual Meeting.
  27. Yibo Miao, Yinpeng Dong, Jun Zhu, Xiao-Shan Gao. Isometric 3D Adversarial Examples in the Physical World, NeurIPS 2022.
  28. X.S. Gao, S. Liu, and L. Yu, Achieve Optimal Adversarial Accuracy for Adversarial Deep Learning using Stackelberg Game, Acta Math Sci (2022).
  29. L. Yu and X.S. Gao, Robust and Information-theoretically Safe Bias Classifier against Adversarial Attacks, arXiv:2111.04404, 2021.
  30. L. Yu and X.S. Gao, A Robust Classification-autoencoder to Defend Outliers and Adversaries, arXiv:2106.15927, 2021.
  31. L. Guo, R.W. Yeung, and X.S. Gao, Proving Information Inequalities and Identities with Symbolic Computation, Proc. IEEE ISIT, 772-777, 2022.
  32. L. Guo, C.M. Yuan, and X.S. Gao, Lower Bound on Derivatives of Costa's Differential Entropy. Entropy, 24, 1155(8), doi/org/10.3390/e24081155 2022.
  33. Qiao-Long Huang and Xiao-Shan Gao, Bit Complexity of Polynomial GCD on Sparse Representation , arXiv:2207.13874, 2022.

    2021

  34. C. Zhao and X.S. Gao, Analyzing the barren plateau phenomenon in training quantum neural network with the ZX-calculus, Quantum, 5, 466, 2021. (arXiv2102.01828)
  35. C. Zhao and X.S. Gao, QDNN: DNN with Quantum Neural Network Layers, Quantum Machine Intelligence, doi: 10.1007/s42484-021-00046-w, 2021, (arXiv:1912.12660)
  36. L. Guo, C.M. Yuan, and X.S. Gao, Lower Bound on Derivatives of Costa's Differential Entropy, Proc. IEEE Int. Symp. Inf. Theory, 1516-1521, 2021. (arXiv:2007.10145)
  37. L. Guo, C.M. Yuan, and X.S. Gao, A Generalization of the Concavity of Renyi Entropy Power, Entropy 2021, 23, 1593. (arXiv:2103.06650)
  38. Y.A. Chen and X.S. Gao. Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems, Journal of Systems Science and Complexity, 2021, DOI: 10.1007/s11424-020-0028-6. (arxiv 1712.06239)
  39. Q.L. Huang and X.S. Gao. Deterministic Interpolation of Sparse Black-box Multivariate Polynomials using Kronecker Type Substitutions (in Chinese), Science China Mathematics (Chinese), 51, 153-166, 2021.
  40. Y. Hu and X.S. Gao, Tropical Differential Groebner Bases, Math. Comput. Sci., 15, 255每269, 2021, 2021.

    2020

  41. Q.L. Huang and X.S. Gao, Faster Interpolation Algorithms for Sparse Multivariate Polynomials Given by Straight-Line Programs, Journal of Symbolic Computation, 101, 367-386, 2020.

    2019

  42. R.J. Jing, C.M. Yuan, X.S. Gao, A Polynomial-time Algorithm to Compute Generalized Hermite Normal Forms of Matrices over Z[x], Theoretical Computer Science, 755(10), 89-109, 2019.
  43. Y. Hu and X.S. Gao, Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems, Journal of Syst. Sci. Complex., 32: 62-77, 2019.
  44. Q.L. Huang and X.S. Gao, Revisit Sparse Polynomial Interpolation based on Randomized Kronecker Substitution, Proc. CASC2019, LNCS 11661, Springer, 216-235, 2019.

    2018

  45. Y.A. Chen and X.S. Gao. Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems, arxiv 1712.06239.
  46. Y.A. Chen, X.S. Gao, C.M. Yuan. Quantum Algorithms for Optimization and Polynomial Systems Solving over Finite Fields, arxiv 1802.03856.

    2017

  47. X.S. Gao, Z. Huang, C.M. Yuan. Binomial difference ideals, Journal of Symbolic Computation, 80(3), 665-706, 2017.
  48. X.S. Gao, Z. Huang, Journal of Wang, C.M. Yuan. Toric Difference Variety, Journal of Syst. Sci. Complex., 30(1), 173-195, 2017.
  49. W. Zhu and X.S. Gao, A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity, Journal of Syst. Sci. Complex., 30(2), 464-483, 2017.
  50. Y.A. Chen and X.S. Gao, Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals, Prof. ISSAC'17, 93-100, ACM Press, 2017.
  51. K. Erkorkmaz, Q.G. Chen, M.Y. Zhao, X. Beudaert, X.S. Gao. Linear programming and windowing based feedrate optimization for spline toolpaths, CIRP Annals - Manufacturing Technology, 66(1),393-396, 2017.
  52. Q. Zhang, X.S. Gao, H.B. Li, M.Y. Zhao. Minimum time corner transition algorithm with confined feedrate and axial acceleration for nc machining along linear tool path, Int J Adv Manuf Techno, 89(1), 941-956, 2017
  53. M.Y. Zhao and X.S. Gao. An Efficient Stochastic Approach for Robust Time-Optimal Trajectory Planning of Robotic Manipulators Under Limited Actuation, Robotica, 35(12), 2400-241, 2017.

    2016

  54. Q. Zhang, S. Li, J.X. Guo, X.S. Gao. Time-optimal path tracking for robots under dynamics constraints based on convex optimization., Robotica, 34(9), 2116每2139, 2016.

    2015

  55. W. Li, C.M. Yuan, X.S. Gao, Sparse Differential Resultant for Laurent Differential Polynomials, Foundations of Computational Mathematics, 15(2), 451-517, 2015.
  56. W. Li, C.M. Yuan, X.S. Gao, Sparse Difference Resultant, Journal of Symbolic Computation, 68, 169-203, 2015.
  57. Z. Yang, L.Y. Shen, C.M. Yuan, X.S. Gao. Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines, Computer-Aided Design, 66, 62-72, 2015.
  58. J.X. Guo, Q. Zhang, X.S. Gao, H. Li. Time Optimal Feedrate Generation with Confined Tracking Error based on Linear Programming, J Syst Sci Complex, 28, 80-95, 2015.
  59. C. Min and X.S. Gao. Iso-scallop Tool-path Generation of 5-axis CNC Machining for Cyclide Patches. Journal of Engineering Manufacture, 229(7), 1144-1156, 2015.
  60. Q. Zhang, S. Li, J.X. Guo, X.S. Gao. Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque, International Journal of Computers, Communications & Control, 10(1), 123-135, 2015.

    2014

  61. J.S. Cheng and X.S. Gao, Multiplicity-preserving triangular set decomposition of two polynomials, J Syst Sci Complex, 27(6), 2014.
  62. Z.Y. Zhang, C.M. Yuan, X.S. Gao, Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials, Computer Mathematics, 479-503, Springer, 2014.

    2013

  63. X.S. Gao, W. Li, C.M. Yuan, Intersection Theory in Differential Algebraic Geometry: Generic Intersections and the Differential Chow Form, Trans. Amer. Math. Soc., 365(9), 4575-4632, 2013.
  64. W. Li, C.M. Yuan, X.S. Gao, Sparse Difference Resultant, Proc. ISSAC 2013, 275-282, ACM Press, New York, 2013. Also arXiv:1111.1084, 2012.
  65. J.X. Guo, K. Zhang, Q. Zhang, X.S. Gao. Efficient Time Optimal Feedrate Planning under Dynamic Constraints for High-order CNC Servo System. Computer-Aided Design, 45(12), 1538-1546, 2013.
  66. K. Zhang, C.M. Yuan, X.S. Gao. Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Technol. 66(9), 1685-1697, 2013.
  67. K. Zhang, Journal of Guo, X.S. Gao. Cubic Spline Trajectory Generation with Axis Jerk and Tracking Error Constraints. Int J Precis Eng Manuf, 14(7), 1141-1146, 2013.
  68. W. Fan, X.S. Gao, C.H. Lee, K. Zhang, Q. Zhang. Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol, 69(5), 1373-1388, 2013.

    2012

  69. X.S. Gao, A Brief Introduction to Computer Mathematics (in Chinese), Bulletin of Chinese Academy of Sciences, 27(2), 189-196, 2012.
  70. J.S. ChengㄛX.S. GaoㄛL. Guo, Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation., Journal of Symbolic Computation, 47 (2012) 843-858.
  71. X.S. Gao and Z. Huang, Characteristic Set Algorithms for Equation Solving in Finite Fields, Journal of Symbolic Computation, 47 (2012) 655每679.
  72. W. Li and X.S. Gao, Chow form for projective differential variety, Journal of Algebra, 370(2012) 344-360.
  73. S.W. Zhao, R. Feng, and X.S. Gao. On Functional Decompisition of Multivariate Polynomials with Differentiation and Homogenization., J Syst Sci Complex, 25(2), 329-347, 2012.
  74. Zhang K., Gao X.S., Li H.B., Yuan C.M. A greedy algorithm for feed-rate planning of CNC machines along curved tool paths with confined jerk for each axis., Robotics and Computer Integrated Manufacturing, 28 (2012) 472-483.
  75. Fan W., Gao X.S., Yan W., Yuan C.M. Interpolation of parametric CNC machining path under confined jounce., Int J Adv Manuf Technol. 62, 719-739, 2012.

    2011

  76. W. Li, X.S. Gao, C.M. Yuan, Sparse Differential Resultant, Proc. ISSAC 2011, 225-232, ACM Press, New York, 2011. (ISSAC Distinguished Paper Award)
  77. M. Zhang, W. Yan, C.M. Yuan, D. Wang, X.S. Gao, Curve fitting and time-optimal interpolation on CNC machines, Science China, Series E, 54(7): 1407-1418, 2011.
  78. L.X. Zhang, R.Y. Sun, X.S. Gao, H. Li, High speed interpolation for micro-line trajectory and adaptive real-time lookahead in CNC machining, Science China, Information Sciences, 54(6), 1481-1495, 2011.
  79. L. Shen, E. Chionh, X.S. Gao, J. Li. Proper Reparametrization for inherently improper unirational varieties., Journal of Systems Science and Complexity, 24(2), 367-380, 2011.
  80. Z. Ye, S.C. Chou, and X.S. Gao. An Introduction to Java Geometry Expert, In Automated Deduction in Geometry, LNAI 6301, 189-195, Springer, 2011.

    2010

  81. Z. Ye, S.C. Chou, X.S. Gao, Visually Dynamic Presentation of Proofs in Plane Geometry, Part 1. Basic Features and the Manual Input Method, Journal of Automated Reasoning, 45, 213-241, 2010.
  82. Z. Ye, S.C. Chou, X.S. Gao, Visually Dynamic Presentation of Proofs in Plane Geometry, Part 2. Automated Generation of Visually Dynamic Presentations with the Full-Angle Method and the Deductive Database Method, Journal of Automated Reasoning, 45, 213-241, 2010.

    2009

  83. X.S. Gao, Y. Luo, and C. Yuan, A Characteristic Set Method for Difference Polynomial Systems, Journal of Symbolic Computation, 44(3), 242-260, 2009.
  84. X.S. Gao, J. Van der Hoeven, C.M. Yuan, G.L. Zhang, Characteristic set method for differential每difference polynomial systems, Journal of Symbolic Computation, 44(9), 2009, 1137-1163.
  85. X.S. Gao, C. Yuan, and G. Zhang, Ritt-Wu's Characteristic Set Method for Ordinary Difference Polynomial Systems with Arbitrary Ordering, Acta Mathematica Scientia, 29(3,4), 1063-1080, 2009.
  86. J.S. Cheng, X.S. Gao, and C.K. Yap, Complete Numerical Isolation of Real Roots in Zero-dimensional Triangular Systems, Journal of Symbolic Computationㄛ 44(7)ㄛ 768-785, 2009.
  87. S.W. Zhao and X.S. Gao, Minimal Achievable Approximation Ratio for MAX-MQ in Finite Fields, Theoretical Computer Science, 410(21-23), 2285-2290, 2009.
  88. M. Zhang and X.S. Gao, Decomposition of ordinary difference polynomials, Journal of Symbolic Computation, 44, 1394-1409, 2009.
  89. J.S. Cheng, X.S. Gao, J. Li, Root Isolation for Bivariate Polynomial Systems with Local Generic Position , Proc. ISSAC 2009, 103-109, ACM Press, New York, 2009.
  90. J.S. Cheng, X.S. Gao, J. Li, Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities, In Computer Algebra in Scientific Computing, LNCS 5743, 89-93, 2009.
  91. J.S. Cheng, X.S. Gao, J. Li, Topology determination and isolation for implicit plane curves. Proc. ACM Symposium on Applied Computing, 1140-1141, ACM Pres, 2009.

    2008

  92. F. Chai, X.S. Gao, and C. Yuan, A Characteristic Set Method for Solving Boolean Equations and Applications in Cryptanalysis of Stream Ciphers, Journal of Systems Science and Complexity, 21(2), 191-208, 2008.
  93. X.S. Gao and M. Zhang, Decomposition of Differential Polynomials, Applicable Algebra in Engineering, Communication and Computing, 19(1), 1-25, 2008.
  94. J. Li, L. Shen, X.S. Gao, Proper Reparametrization of Rational Ruled Surface, Journal of Computer Science and Technology, 23(2), 290-297, 2008.
  95. G.L. Zhang and X.S. Gao, Properties of Ascending Chians fr Partial Difference Polynomial Systems, ASCM2007, LNAI 5081, 307-321, Springer-Verlag, Berlin Heidelberg, 2008.

    2007

  96. W.T. Wu and X.S. Gao, Mathematics Mechanization and Applications After Thirty Years, Frontiers in Computer Science, 1(1), 1-8, 2007.
  97. J.S. Cheng, X.S. Gao, and C.K. Yap, Complete Numerical Isolation of Real Zeros in General Triangular Systems, ISSAC 2007, 92-99, ACM Press, New York, 2007.
  98. X. Zhao and X.S. Gao, Binary Affinity Genetic Algorithmㄛ Journal of Heuristics, 13, 133-150, 2007.
  99. X. Zhao, X.S. Gao, and Z. Hu, Evolutionary Programming Based on Non-uniform MutationㄛApplied Mathematics and Computation, 192(1), 1-11, 2007.

    2006

  100. R.Y. Feng and X.S. Gao, A Polynomial Time Algorithm To Find Rational General Solutions Of First Order Autonomous ODEs, Journal of Symbolic Computation, 41(7), 739-762, 2006.
  101. E.W. Chionh, X.S. Gao and L.Y. Shen, Inherently improper surface parametric supports, Computer Aided Geometric Design, 23, 629-639, 2006.
  102. X.S. Gao, Q. Lin, and G. Zhang, A C-tree Decomposition Algorithm for 2D and 3D Geometric Constraint Solving, Computer-Aided Design, 38(1), 1-13, 2006.
  103. X.S. Gao and C. Yuan, Resolvent Systems of Difference Polynomial Ideals, Proc. ISSAC 2006, ACM Press, New York, 2006.
  104. X.S. Gao and J. Tang, On the Probability of the Number of Solutions for the P4P Problem, Journal of Mathematical Imaging and Vision, 25, 79-86, 2006.
  105. M. Li, X.S. Gao, and S.C. Chou, Quadratic Approximation to Plane Parametric Curves and Applications in Approximate Implicitization, Visual Computers, 22, 906-917, 2006.
  106. G.F. Zhang and X.S. Gao, Well-constrained Completion and Decomposition for Under-constrained Geometric Constraint Problems, 16, International Journal of Computational Geometry & Applications, 461-478, 2006.
  107. G.F. Zhang and X.S. Gao, Planar Generalized Stewart-Gough Platforms and their Direct Kinematics, ADG 2004, LNAI 3763, 198-211, Springer-Verlag, Berlin, 2006,.
  108. G.F. Zhang and X.S. Gao, Spatial Geometric Constraint Solving Based on k-connected Graph Decomposition, 973-977, Proc. of The 21st Annual ACM Symposium on Applied Computing, Dijon, France, ACM Press, 2006.
  109. J. Li and X.S. Gao, The Proper Parametrization of a Special Class of Rational Parametric Equations, Journal of of Sys. Sci. and Complexity, 19, 331-339, 2006.

    2005

  110. X.S. Gao, D. Lei, Q. Liao, and G. Zhang, Generalized Stewart Platforms and their Direct Kinematics, IEEE Trans. Robotics, vol 21, 141-151, 2005.
  111. J.M. Aroca, J.Cano R. Feng and X.S. Gao, Algebraic general solutions of algebraic ODEs, Proc. ISSAC2005, 29-36ㄛACM Press, New York, 2005.
  112. J.S. Cheng, X.S. Gao, and M. Li, Determine the Topology of Real Algebraic Surfaces, Mathematics of Surfaces, 121-146, LNCS, Springer-Verlag, 2005.
  113. M. Li, X.S. Gao, and J.S. Cheng, Generating Symbolic Interpolants for Scattered Satat with Normal Vectors, Journal of Computer Science and Technology, 20, 861-874 2005.

    2004

  114. X.S. Gao and K. Jiang, Survey on Geometric Constraint Solving (in Chinese), Journal of of CAD & CG, 16(4), 385-396, 2004.
  115. X.S. Gao, C.M. Hoffmann and W. Yang, Solving spatial basic geometric constraint configurations with locus intersection, Computer Aided Design, 111-122, 36(2), 2004.
  116. X.S. Gao and M. Li, Rational Quadratic Approximation to Real Algebraic Curves, Computer Aided Geometric Design, 21, 805-828, 2004.
  117. X.S. Gao and Q. Lin, MMP/Geometer - A Software Package for Automated Geometry Reasoning, Automated Deduction in Geometry, (ed. F. Winkler), 44-66, Springer, Berlin, 2004.
  118. Journal of Wang and X.S. Gao, An Algorithm for Solving Partial Differential Parametric Systems, Discrete Applied Mathematics. 136(1), 105-116, 2004.
  119. R. Feng and X.S. Gao, Rational General Solutions of Algebraic Ordinary Differential Equations, Proc. ISSAC2004, 155-162, ACM Press, New York, 2004.
  120. X.S. Gao and M. Zhang, Decomposition of Differential Polynomials with Constant Coefficients, Proc. ISSAC2004, 175-182, ACM Press, New York, 2004.
  121. F. Xie and X.S. Gao, Applications of Computer Algebra in Solving Nonlinear Evolution Equations, Commun. Theor. Phys. 41 (2004) 353-356.

    2003

  122. X.S. Gao, X. Hou, J. Tang and H. Chen, Complete Solution Classification for the Perspective-Three-Point Problem, IEEE Tran. on PAMI, 930-943, 25(8), 2003..
    Here is the appendix to this paper
  123. X.S. Gao, Implicitization for Differential Rational Parametric Equations, Journal of of Symbolic Computation, 811-824, 36(5), 2003..
  124. Y. Chen and X.S. Gao, Involutive Bases of Algebraic Partial Differential Equation Systems, Science in China (A), 33(2), 97-113, 2003.
  125. X.S. Gao and D.K. Wang, Zero Decomposition Theorems for Counting the Number of Solutions for Parametric Equation Systems, in Computer Mathematics, Proc. of ASCM2003, (eds. Z. Li and W. Sit), 130-145, World Scientific, Singapore, 2003.
  126. X.S. Gao and G. Zhang, Geometric Constraint Solving via C-tree Decomposition, (Appendix) ACM Solid Modelling 2003, 45-55, Seattle, USA, ACM Press, New York, 2003.

    2002

  127. X.S. Gao, K. Jiang, and C.-C. Zhu, Geometric Constraint Solving with Conics and Linkages, Computer Aided Design, 34(6), 421-433, 2002.
  128. X.S. Gao, C. Zhu, S.-C. Chou, and J.-X. Ge, Automated Generation of Kempe Linkages for Algebraic Curves and Surfaces, Mechanism and Machine Theory, 36(9), 1019-1033, 2002.
  129. T. Chaolu and X.S. Gao, Nearly Differential Characteristic Set for Differential Polynomial System, Acta Mathematica Sinica, 45(6), 1041-1050, 2002.
  130. X.S. Gao and T. Xu, Luroth's Theorem in Differential Fields, Journal of Sys. Sci. and Complexity, 15(4), 376-383, 2002.
  131. X.S. Gao, C.M. Hoffmann and W. Yang, Solving Basic Gometric Constraint Configurations with Locus Intersection, Proc. ACM Solid Modelling 2002, 95-104, ACM Press, New York, 2002.

    2001

  132. S.C. Chou and X.S. Gao, Automated reasoning in geometry, Handbook of Automated Reasoning, (eds. A. Robinson and A. Voronkov), 709-749, Elsevier, Amsterdam, 2001.
  133. X.S. Gao, Mathematics Mechanization: A Survey (In Chinese), Advances in Mathematics, 30(5), 385-404, 2001.
  134. Y.F. Chen and X.S. Gao, Involutive Directions and New Involutive Divisions, Computers and Mathematics with Applications, 41(7-8), 2001, 945-956.
  135. X.S. Gao, L. Huang, and K, Jiang, Geometric Constraint Solving with Geometric Transformation, Science in China (Series F), 44(1), 50-59, 2001.
  136. X.S. Gao, L. Huang, and K, Jiang, A Hybrid Method for Solving Geometric Constraint Problems in Automated Deduction in Geometry, Journal of Richter-Gebert and D. Wang (eds), 16-25, LNAI No. 2061, Springer-Verlag, Berlin, 2001.

    2000

  137. J. Ge, S.C. Chou and X.S. Gao, Geometric Constraint Satisfaction Using Optimization Methods, Computer Aided Design, 31(14), 867-879, 2000.
  138. S.C. Chou, X.S. Gao, and J.Z. Zhang, A Deductive Database Approach To Automated Geometry Theorem Proving and Discovering, Journal of Automated Reasoning, 25(3), 219-246, 2000.
  139. X.S. Gao and K. Jiang, Order in Solving Polynomial Equations, Computer Mathematics, Proc. of ASCM'2000, pp. 308-318, World Scientific, 2000.
  140. X.S. Gao, W.Q. Yang, and L. Huang, Intelligent Dynamic Geometry, Proc. ATCM'2000, ATCM Inc, Thailand, pp.162-171.

    1999

  141. X.S. Gao and S. C. Chou, On the Theory of Resolvents and Its Applications, Sys. Sci. and Math. Sci., 12, Suppl., 17--30, 1999,
  142. X.S. Gao, Automated Geometry Diagram Construction and Engineering Geometry, in Automated Deduction in Geometry, Proc. of ADG98, pp. 226-252, Springer, 1999.
  143. X.S. Gao, Building Dynamic Mathematical Models with Geometry Expert, III. A Geometry Deductive Database Proc. Of ATCM'99, 153-162, 1999, ATCM Inc., USA.

    1998

  144. X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, I. A Global Propagation Approach, Computer Aided Design, Vol. 30, No. 1, 47-54, 1998.
  145. X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, II. A Symbolic Computational Approach, Computer Aided Design, Vol. 30, No.2, 115-122, 1998.
  146. L. Yang, X.S. Gao, S. C. Chou, and Z. J.Z. Zhang, Automated Proving and Discovering of Theorems in Non-Euclidean Geometries, in: Automated Deduction in Geometry, LNAI 1360, Springer-Verlag, Berlin Heidelberg, 1998, pp. 171--188.
  147. X.S. Gao, C. C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, I. Geometric Transformations, Functions and Plane Curves, Proceedings of the Third Asian Technology Conference in Mathematics, eds W.C. Yang, pp. 216-224, Springer, 1998.
  148. X.S. Gao, C. C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, II. Linkages, Proc. of the Third Asian Symposium on Computer Mathematics, eds Z. B. Li, pp. 15-22, LanZhou University Press, 1998.

    1996

  149. S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of Readable Proofs with Geometric Invariants, I. Multiple and Shortest Proof Generation, Journal of of Automated Reasoning, 17, 325-347, 1996.
  150. S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of Readable Proofs with Geometric Invariants, II. Proving Theorems with Full-Angles, Journal of of Automated Reasoning, 17, 349-370, 1996.
  151. S.C. Chou, X.S. Gao, and J.Z. Zhang, An Introduction to Geometry Expert, Proc. CADE-13, p. 235-239, 1996, L.N.A.I. No. 1104, (eds. M. A. McRobbie and Journal of K. Slaney), Springer-Verlag.

    1995

  152. S.C. Chou, X.S. Gao, J.Z. Zhang, Automated Production of Traditional Proofs in Solid Geometry, Journal of Automated Reasoning, 14, p.257-291, 1995.
  153. S.C. Chou, X.S. Gao, and Journal of Z. Zhang, ``Automated Production of Traditional Proofs for Theorems in Euclidean Geometry, Part I. The Hilbert Intersection Point Theorems'', Annals of Mathematics and Artificial Intelligence, 13, (1995), p.109-137.
  154. X.S. Gao and S.C. Chou, The Computer Searches for Pascal Conics, Journal of Computers and Mathematical Applications, Vol. 29, No. 2, pp. 63-71, 1995.
  155. X.S. Gao and D.K. Wang, On the Automatic Derivation of a Set of Geometric Formulae, Journal of Geometry, vol. 53, p.79-88, 1995.

    1994

  156. S.C. Chou, X.S. Gao, N.M. Mcphee, and S. C. Chou, ``Mechanically Proving Geometry Theorems Using a Combination of Wu's Method and Collins' Method'', in Proceedings of CADE-12, Nancy, France, June 1994, 222--236.

    1993

  157. X.S. Gao and S. C. Chou, A Zero Structure Theorem for Differential Parametric Systems, Journal of Symbolic Computation, Vol. 16, 585-595, 1993.
  158. X.S. Gao and S. C. Chou, The Dimension of Ascending Chains, Chinese Science Bulletin, Vol. 38, No.5, 1993, 396--399.
  159. S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part I. An Improved Version of Ritt--Wu's Decomposition Algorithm , Journal of Automated Reasoning, 10: 161--172, 1993.
  160. S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part II. Mechanical Theorem Proving, Journal of Automated Reasoning, 10: 173--189, 1993.
  161. S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part IV, Bertrand Curves , Journal of Sys. and Math., vol. 6, p.186-192, 1993.
  162. S.C. Chou, X.S. Gao, J.Z. Zhang, ``Automated Geometry Theorem Proving by Vector Calculation'', Proceedings of ISSAC-93, 284-291.
  163. S.C. Chou, X.S. Gao, J.Z. Zhang, Automated Production of Traditional Proofs for Theorems in Euclidean Geometry, Proc. of 8th IEEE Symposium on Logic in Computer Science (LICS), extended abstract, 1993, 48--56.

    1992

  164. S.C. Chou and X.S. Gao, Implicitization of Rational Parametric Equations, Journal of Symbolic Computation, 1992, 14, 459--470.
  165. S.C. Chou and X.S. Gao, On the Parameterization of Algebraic Curves, Journal of Applicable Algebra in Engineering, Communication and Computing, 3, 27--38 (1992).
  166. S.C. Chou and X.S. Gao, Proving Geometry Statements of Constructive Type, in Proceedings of CADE-11, Lecture Notes in Computer Science, Vol. 607, 20--34, Springer--Verlag, 1992.
  167. S.C. Chou, X.S. Gao, and D.S. Arnon, On the Mechanical Proof Geometry Theorems Involving Inequalities' Advances in Computing Research, 1992, Vol. 6, 139--181.
  168. Transformation Theorems among Caley-Klein Geometries, Journal of of Sys. Sci. and Math. Sci., 1992, 3: 260--273.
  169. SC Chou and XS Gao, Automated Reasoning in Differential Geometry and Mechanics Using the Characteristic Set Method; Part III Mechanical Formula Derivation, in Proceedings of the IFIP International Workshop on Automated Reasoning, Elsevier Science Publishers (North--Holland), Beijing, p1--12, 1992.
  170. SC Chou and XS Gao, Solving Parametric Algebraic Systems, in the Proceedings of ISSAC'92 , Berkeley, 335--341, ACM Press, 1992.
  171. SC Chou and XS Gao, ``An Algebraic System Based on the Characteristic Set Method'', in Proceedings of International Workshop on Mathematics Mechanization, Beijing, International Academic Publishers, p.1--17, 1992.

    1991

  172. X.S. Gao and S.C. Chou, Computations with Parameter Equations, in Prof. ISSAC'91, Germany, ACM Press, 122--127, 1991.
  173. X.S. Gao and S.C. Chou, On the Normal Parameterization of Curves and Surfaces, The International Journal of Computational Geometry & Applications, Vol. 1, No. 2 (1991), 125--136.
  174. X.S. Gao, The Discriminant Systems of Univariate Polynomials and Their Computations, Chinese Quarterly Journal of Mathematics, No2., p1-p11, 1991.
  175. X.S. Gao, Transcendental Functions and Mechanical Theorem Proving in Elementary Geometries, Journal of Automated Reasoning, 6:403-417, 1990, Kluwer Academic Publishers.

    Before 1990

  176. S.C. Chou and X.S. Gao, Methods for Mechanical Geometry Formula Deriving in Proceedings of ISSAC'90 , Japan, ACM Press, August 1990, 265--270.
  177. S.C. Chou and X.S. Gao, Ritt-Wu's Decomposition Algorithm and Geometry Theorem Proving in Proceedings of CADE--10, Lecture Notes in Artificial Intelligence 449, Springer--Verlag, 1990, 207--220.
  178. X.S. Gao, The Minimal Characteristic Basis of a Differential Polynomial Ideal, Chinese Science Bulletin, vol. 35, No. 6, 1990, 455-458.
  179. X.S. Gao, The Minimal Characteristic Basis of a Polynomial Ideal, Journal of Sys Sci & Math Sci, No.2, 1989, 236-242.
  180. X.S. Gao, Trigonometric Identities and Mechanical Theorem Proving in Elementary Geometries, Journal of Sys. Sci. & Math. Sci. No.3 1987.

    Collection of Geometric Problems

  181. S.C. Chou, X.S. Gao, and J.Z. Zhang, A Collection of 130 Geometric Constraint Problems and Their Solutions, WSUCS-96-2, CS Dept, Wichita State University, 1996.

Conference Abbreviation

ACM SM: ACM Symposium on Solid Modeling
ADG: Automated Dedecution in Geometry
ASCM: Asian Symposium on Computer Mathematics
ATCM: Asian Technology Conference on Mathematics
CADE: An International Conference on Automated Deduction
GMP: Geometric Modeling and Processing
ISSAC: International Symposium on Symbolic and Algebraic Computation
LICS: IEEE Symposium on Logic in Computer Science
SMI: International Conference on Shape Modelling