夏壁灿 (Bican Xia)

中文

Selected Publications

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65. T. Gan, M. Chen, Y. Li, B. Xia and N. Zhan: Reachability Analysis for Solvable Dynamical Systems. Accepted by IEEE Transactions on Automatic Control.

 

64. Y. Feng, L. Zhang, D. N. Jansen, N. Zhan and B. Xia: Finding Polynomial Loop Invariants for Probabilistic Programs. In: D. D'SouzaK and K. Narayan Kumar (Eds.): ATVA 2017, LNCS 10482, pp.400--416, 2017.

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63. Y. Wang, W. Wu and B. Xia: A Special Homotopy Continuation Method For A Class of Polynomial Systems. In: V.P. Gerdt et al. (Eds.): CASC 2017, LNCS 10490, pp. 362--376, 2017.  

62. Q. Wang, Y. Li, B. Xia and N. Zhan: Generating Semi-Algebraic Invariants for Non-Autonomous Polynomial Hybrid Systems. J. Syst. Sci. Complex, 30: 234--252, 2017.

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61. Bican Xia and Lu Yang: Automated Inequality Proving and Discovering. World Scientific, 344 pages, Aug. 2016. pdf

60. T. Gan, L. Dai, B. Xia, N. Zhan, D. Kapur and M. Chen: Interpolation synthesis for quadratic polynomial inequalities and combination with EUF. N. Olivetti and A. Tiwari (Eds.): IJCAR 2016, LNAI 9706, pp. 195–212, 2016. arXiv:1601.04802v2

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59. T. Gan, M. Chen, Y. Li, B. Xia and N. Zhan: Computing Reachable Sets of Linear Vector Fields Revisited. Proc. European Control Conference (ECC'2016), pp. 419--426. June 29 - July 1, 2016. Aalborg, Denmark.

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58. T. Gan, M. Chen, L. Dai, B. Xia and N. Zhan: Decidability of the Reachability for a Family of Linear Vector Fields. Proc. of ATVA'2015, LNCS 9364, 482--499, 2015.

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57. J. Han, L. Dai, H. Hong and B. Xia: Open weak cad and its applications. arXiv:1507.03834. Journal of Symbolic Computation, vol. 80: 785–816, 2017.

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56. L. Dai and B. Xia: Smaller SDP for SOS Decomposition.  arXiv:1407.2679v2 [math.OC]. Journal of Global Optimization, vol. 63: 343--361, 2015.

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55. Z. Chen, X. Tang and B. Xia: Hierarchical Comprehensive Triangular Decomposition. In: Mathematical Software – ICMS 2014, LNCS 8592, 2014, pp 434-441.  arXiv:1406.0599v1 [cs.SC]

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54. J. Han, L. Dai and B. Xia: Constructing Fewer Open Cells by GCD Computation in CAD Projection. In: Proc. ISSAC 2014, 240--247, ACM Press, 2014. arXiv:1401.4953v1.

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53. H. Hong, X. Tang and B. Xia: Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems. Journal of Symbolic Computation, Vol. 70: 112–135, 2015.

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52. L. Dai, T. Gan, B. Xia and N. Zhan: Barrier Certificates Revisited. arXiv:1310.6481. Journal of Symbolic Computation, vol. 80: 62--86, 2017.

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51. Z. She, H. Li, B. Xue, Z. Zheng and B. Xia: Discovering polynomial Lyapunov functions for continuous dynamical systems. Journal of Symbolic Computation, Vol.58: 41--63, 2013.

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50. Z. Chen, X. Tang and B. Xia: Generic regular decompositions for parametric polynomial systems. arXiv:1301.3991v1. Journal of Systems Science and Complexity, 28(5): 1194--1211, 2015.

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49. L. Dai, B. Xia and N. Zhan: Generating non-linear interpolants by semi-definite programming. In: N. Sharygina and H. Veith (Eds.): CAV 2013, LNCS 8044, pp. 364--380, Springer, Heidelberg (2013).

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48. C. Chen, J. Davenport, M. Moreno Maza, B. Xia and R. Xiao: Computing with semi-algebraic sets: Relaxation techniques and effective boundaries. Journal of Symbolic Computation, Vol. 52: 72--96, 2013.

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47. C. Chen, J. Davenport, J. P. May, M. Moreno Maza, B. Xia and R. Xiao: Triangular decomposition of semi-algebraic systems. Journal of Symbolic Computation, vol. 49: 3--26, 2013.

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46. Liyun Dai and Bican Xia: logcf: An Efficient Tool for Real Root Isolation. arXiv:1209.3555 [cs.SC]

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45. Xiaoxian Tang, Zhenghong Chen, Bican Xia: Generic Regular Decompositions for Generic Zero-Dimensional Systems. arXiv:1208.6112v3 [cs.SC]. Science China: Information Sciences, vol. 57, No. 9, 1--14, 2014.

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44. Jingjun Han, Zhi Jin and Bican Xia: Proving Inequalities and Solving Global Optimization Problems via Simplified CAD Projection. arXiv:1205.1223v4 [cs.SC]. Journal of Symbolic Computation, vol. 72, pp. 206--230, 2016.

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43.Fei Shen, Wenyuan Wu and Bican Xia: Real Root Isolation of Polynomial Equations Based on Hybrid Computation. arXiv:1207.3019v1 [cs.SC]. In: Computer Mathematics - Proc. ASCM2012, pp. 375--396, Springer, 2014.

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42. Liyun Dai and Bican Xia: Non-termination Sets of Simple Linear Loops. In: A. Roychoudhury and M. D'Souza (Eds.): ICTAC 2012, LNCS 7521, pp 61-73, 2012.

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41. C. Chen, J. H. Davenport, F. Lemaire, M. Moreno Maza, B. Xia, R. Xiao, Y. Xie: Computing the real solutions of polynomial systems with the RegularChains library in Maple. Software Demo at ISSAC 2011, Communications in Computer Algebra , Volume 45 Issue 3/4, 2012.

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40. C. Chen, J. Davenport, M. Moreno Maza, B. Xia and R. Xiao: Computing with Semi-Algebraic Sets Represented by Triangular Decomposition, Proc. ISSAC 2011, 75--82, ACM Press, 2011.

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39. Y. Li, B. Xia, Z. Zhang: Zero decomposition with multiplicity of zero-dimensional polynomial systems. arXiv:1011.1634 [cs.SC], Nov. 7, 2010.

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38. C. Chen, J. Davenport, J. P. May, M. Moreno Maza, B. Xia and R. Xiao: Triangular decomposition of semi-algebraic systems, Proc. ISSAC 2010, ACM Press, 187--194.

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37. B. Xia, Z. Zhang: Termination of Linear Programs with Nonlinear Constraints, Journal of Symbolic Computation , 45(2010): 1234--1249.

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36. L. Yang, C. Zhou, N. Zhan, B. Xia: Recent advances in program verification through computer algebra, Frontiers of Computer Science in China, 2010, 4(1): 1--16.

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35. B. Xia, L. Yang, N. Zhan, Z. Zhang: Symbolic decision procedure for termination of linear programs. (DOI: 10.1007/s00165-009-0144-5), Formal Aspects of Computing, 23(2): 171--190, 2011.

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34. Z. Zhang, T. Fang, B. Xia: Real Solution Isolation with Multiplicity of Zero-Dimensional Systems. Science China Information Sciences, 2011, Vol. 54(1):60--69.

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33. C. Chen, M. Moreno Maza, B. Xia, L. Yang: Computing Cylindrical Algebraic Decomposition via Triangular Decomposition. ISSAC'09, ACM Press, 95--102.

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32. Z. She, B. Xia, R. Xiao, Z. Zheng: A Semi-algebraic Approach for asymptotic stability analysis. Nonlinear Analysis: Hybrid Systems, 3(2009) , 588--596.

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31. Bican Xia, Lu Yang, Naijun Zhan: Program Verification by Reduction to Semi-Algebraic Systems Solving. Proceedings of ISoLA 2008, CCIS 17 (T. Margaria and B. Ste en Eds.), Springer-Verlag, pp277-291, 2008.

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30. 《Automated Proving and Discovering on Inequalities》(in Chinese), Science Press, Beijing, January, 2008.

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29. Ting Zhang and Bican Xia: A New Method for Real Root Isolation of Univariate Polynomials. Mathematics in Computer Science, Vol. 1, 305—320, 2007.

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28. D. Wang, B. Xia and Z. Li, 《Computer Algebra》(in Chinese), Second Edition, Tsinghua University Press, Oct., 2007.

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27. Q. Guan, L. Wang, B. Xia, L. Yang, W. Yu and Z. Zeng, Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems, Science in China Ser. F, Vol. 50, no. 5, 719--731.

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26. B. Xia: DISCOVERER: A tool for solving semi-algebraic systems, Software Demo at ISSAC 2007, Waterloo, July 30, 2007. Also: ACM SIGSAM Bulletin, Vol. 41, No. 3, pp.102--103, Sept., 2007.

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25. Y. Chen, B. Xia, L. Yang, N. Zhan, C. Zhou, Discovering Non-linear Ranking Functions by Solving Semi-algebraic Systems, LNCS 4711, p.34--p.49, 2007.

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24. Y. Chen, B. Xia, L. Yang, N. Zhan, Generating polynomial invariants with DISCOVERER and QEPCAD, LNCS 4700, p.67--p.82, 2007.

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23. S. Ning, B. Xia, Z. Zheng, On a cubic system with eight limit cycles, Bulletin of the Belgian Mathematical Society Simon Stevin, Vol. 14, 595--605, 2007.

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22. She Zhikun, Xia Bican and Xiao Rong, A Semi-algebraic Approach for the Computation of Lyapunov Functions, in: Proc. The Second IASTED International Conference on Computational Intelligence (CI 2006) (B. Kovalerchuk ed.), pp.7—12, ACTA Press Anaheim, USA, 2006.

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21. Yang Lu and Xia Bican, Quantifier Elimination for Quartics. In: Lecture Notes in Artificial Intelligence 4120 (T. Ida, J. Calmet and D. Wang eds.), pp. 131—145, Sept. 2006.

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20. Xia Bican and Zhang Ting, Real Solution Isolation Using Interval Arithmetic, Computers and Mathematics with Applications, Vol. 52, pp.853—860, 2006.

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19. Zhang Ting and Xia Bican: A new method for real root isolation of univariate polynomials, Proc. the First International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS05), pp.85—91, Beijing, July 24-26, 2006.

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18. Yang Lu, Zhan Naijun, Xia Bican and Zhou Chaochen: Program Verification by Using DISCOVERER. Position paper in Verified Software: Theories, Tools, Experiments (VSTTE 2005), ETH Zürich, Oct. 10-13, 2005. In LNCS 4171, pp.528--538, 2008.

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17. Zhang Ting, Xiao Rong and Xia Bican: Real Solution Isolation Based on Interval Krawczyk Operator. Proc. the 7th Asian Symposium on Computer Mathematics (ASCM 2005), (Sung-il Pae, H. Park, eds.), pp.235—237. Seoul, Dec.8-10, 2005.

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16. Xia Bican, Xiao Rong and Yang Lu: Solving parametric semi-algebraic systems. Proc. the 7th Asian Symposium on Computer Mathematics (ASCM 2005), (Sung-il Pae, H. Park, eds.), pp.153—156. Seoul, Dec.8-10, 2005.

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15. Wang Dongming and Xia Bican: Algebraic Analysis of Stability for Some Biological Systems. In: Algebraic Biology 2005 - Computer Algebra in Biology (Proceedings of the First International Conference, Tokyo, Japan, November 28-30, 2005) (H. Anai and K. Horimoto, eds.), Universal Academy Press, Inc., Tokyo, 2005, pp. 75—83.

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14. Wang Dongming, Xia Bican: Stability analysis of biological systems with real solution classification. In: Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (ISSAC 2005) (M. Kauers, ed.), pp. 354—361. ACM Press, New York (2005).

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13. Yang Lu, Xia Bican: Real solution classifications of a class of parametric semi-algebraic systems. In: Algorithmic Algebra and Logic --- Proceedings of the A3L 2005 (A. Dolzmann, A. Seidl, and T. Sturm, eds.), pp. 281—289. Herstellung und Verlag, Norderstedt (2005).

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12. Bican Xia and Lu Yang: A New Result on the p-Irreducibility of Binding Polynomials, Computers and Mathematics with Applications, Vol. 48, 1811—1817, 2004.

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11. Yang Lu, Xia Bican, Automated Deduction in Geometry, in Geometric Computation, World Scientific, pp.248--298, 2004.

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10. D. Wang and B. Xia, 《Computer Algebra》(in Chinese), Tsinghua University Press, July 2004.

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9. Two chapters in 《Selected lectures in Symbolic Computation》(in Chinese) (D. Wang ed.), Tsinghua University Press, 2003.

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8. Xia Bican and Yang Lu, An algorithm for isolating the real solutions of semi-algebraic systems, J. of Symbolic Computation, Vol. 34, No.5, pp.461-477, 2002.

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7. Xia Bican and Hou Xiaorong, A Complete Algorithm for Counting Real Solutions of Polynomial Systems of Equations and Inequalities, Computers & Mathematics with Applications, Vol. 44, pp.633-642, 2002.

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6. She Zhikun, Xia Bican, Zheng Zhiming, Pseudo-Division Machine (I): A Model of Symbolic Computation, in Proceedings of the First International Congress of Mathematical Software, pp.115-125, World Scientific, 2002.

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5. Xia Bican and Yang Lu, An effective algorithm for isolating the real solutions of semi-algebraic systems and its applications, in Computer Mathematics-- Proceedings of the ASCM’2001 (K. Shirayanagi and K. Yokoyama eds.), pp.211-220, World Scientific, Singapore, September, 2001.

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4. Yang Lu, Hou Xiaorong and Xia Bican, A complete algorithm for automated discovering of a class of inequality-type theorems, Science in China, Series F, Vol. 44, No. 1, pp.33-49, 2001.

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中文

3. Xia Bican, DISCOVERER: A tool for solving problems involving polynomial inequalities, in Proceedings of the ATCM’2000 (Wei-Chi Yang, et al. eds.), pp.472-481, ATCM Inc., Blacksburg, USA, Dec, 2000.

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2. Yang Lu and Xia Bican, An Explicit Criterion to Determine the Number of Roots in an Interval of a Polynomial, Progress in Natural Science, Vol.10, No. 12, pp897-910, 2000.

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1. Lu Yang, Xiaorong Hou & Bican Xia, Automated Discovering and Proving for Geometric Inequalities, in Lecture Notes in Artificial Intelligence 1669, Springer-Verlag, pp.30-46, 1999.

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