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Volumn 4711 LNCS, Issue , 2007, Pages 34-49

Discovering non-linear ranking functions by solving semi-algebraic systems

Author keywords

Computer algebra; DISCOVERER; Loop termination; Polynomial programs; Program verification; QEPCAD; Ranking function; Semi algebraic systems

Indexed keywords

ALGEBRA; CALCULATIONS; DIFFERENCE EQUATIONS; POLYNOMIAL APPROXIMATION;

EID: 38049158356     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-75292-9_3     Document Type: Conference Paper
Times cited : (77)

References (27)
  • 1
    • 33749837789 scopus 로고    scopus 로고
    • Braverman, M.: Termination of integer linear programs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, 4144, pp. 372-385. Springer, Heidelberg (2006)
    • Braverman, M.: Termination of integer linear programs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 372-385. Springer, Heidelberg (2006)
  • 2
    • 24144470050 scopus 로고    scopus 로고
    • Terminaition of polynomial programs
    • Cousot, R, ed, VMCAI 2005, Springer, Heidelberg
    • Bradley, A., Manna, Z., Sipma, H.: Terminaition of polynomial programs. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 113-129. Springer, Heidelberg (2005)
    • (2005) LNCS , vol.3385 , pp. 113-129
    • Bradley, A.1    Manna, Z.2    Sipma, H.3
  • 3
    • 33749830015 scopus 로고    scopus 로고
    • Cook, B., Podelski, A., Rybalchenko, A.: TERMINATOR: Beyond safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, 4144, pp. 415-418. Springer, Heidelberg (2006)
    • Cook, B., Podelski, A., Rybalchenko, A.: TERMINATOR: Beyond safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 415-418. Springer, Heidelberg (2006)
  • 4
    • 80052985571 scopus 로고
    • Partial cylindrical algebraic decomposition for quantifier elimination
    • Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. J. of Symbolic Computation 12, 299-328 (1991)
    • (1991) J. of Symbolic Computation , vol.12 , pp. 299-328
    • Collins, G.E.1    Hong, H.2
  • 5
    • 84903179505 scopus 로고    scopus 로고
    • Synthesis of linear ranking functions
    • Margaria, T, Yi, W, eds, ETAPS 2001 and TACAS 2001, Springer, Heidelberg
    • Colón, M., Sipma, H.B.: Synthesis of linear ranking functions. In: Margaria, T., Yi, W. (eds.) ETAPS 2001 and TACAS 2001. LNCS, vol. 2031, pp. 67-81. Springer, Heidelberg (2001)
    • (2001) LNCS , vol.2031 , pp. 67-81
    • Colón, M.1    Sipma, H.B.2
  • 6
    • 24144488686 scopus 로고    scopus 로고
    • Proving program invariance and termination by parametric abstraction, Langrangian Relaxation and semidefinite programming
    • Cousot, R, ed, VMCAI 2005, Springer, Heidelberg
    • Cousot, P.: Proving program invariance and termination by parametric abstraction, Langrangian Relaxation and semidefinite programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 1-24. Springer, Heidelberg (2005)
    • (2005) LNCS , vol.3385 , pp. 1-24
    • Cousot, P.1
  • 9
    • 0002443040 scopus 로고    scopus 로고
    • REDLOG: Computer algebra meets computer logic
    • Dolzman, A., Sturm, T.: REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31(2), 2-9
    • ACM SIGSAM Bulletin , vol.31 , Issue.2 , pp. 2-9
    • Dolzman, A.1    Sturm, T.2
  • 11
    • 84945708698 scopus 로고
    • An axiomatic basis for computer programming
    • Hoare, C.A.R.: An axiomatic basis for computer programming. Comm. ACM 12(10), 576-580 (1969)
    • (1969) Comm. ACM , vol.12 , Issue.10 , pp. 576-580
    • Hoare, C.A.R.1
  • 13
    • 84944228451 scopus 로고    scopus 로고
    • A complete method for the synthesis of linear ranking functions
    • Steffen, B, Levi, G, eds, VMCAI 2004, Springer, Heidelberg
    • Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239-251. Springer, Heidelberg (2004)
    • (2004) LNCS , vol.2937 , pp. 239-251
    • Podelski, A.1    Rybalchenko, A.2
  • 14
    • 2442424185 scopus 로고    scopus 로고
    • Non-linear loop invariant generation using Gröbner bases
    • Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Non-linear loop invariant generation using Gröbner bases. In: ACM POPL'04, pp. 318-329 (2004)
    • (2004) ACM POPL'04 , pp. 318-329
    • Sankaranarayanan, S.1    Sipma, H.B.2    Manna, Z.3
  • 16
    • 35048871890 scopus 로고    scopus 로고
    • Tiwari, A.: Termination of linear programs. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, 3114, pp. 70-82. Springer, Heidelberg (2004)
    • Tiwari, A.: Termination of linear programs. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 70-82. Springer, Heidelberg (2004)
  • 17
    • 38049148091 scopus 로고    scopus 로고
    • International Conference on Verified Software:, ETH Zürich October 10-13
    • International Conference on Verified Software: Theories, Tools and Experiments, ETH Zürich (October 10-13, 2005)
    • (2005) Theories, Tools and Experiments
  • 18
    • 0000060015 scopus 로고
    • Basic principles of mechanical theorem proving in elementary geometries
    • Wu, W.-T.: Basic principles of mechanical theorem proving in elementary geometries. J. Syst. Sci. Math. 4, 207-235 (1984)
    • (1984) J. Syst. Sci. Math , vol.4 , pp. 207-235
    • Wu, W.-T.1
  • 20
    • 0036851606 scopus 로고    scopus 로고
    • An algorithm for isolating the real solutions of semi-algebraic systems
    • Xia, B., Yang, L.: An algorithm for isolating the real solutions of semi-algebraic systems. J. Symbolic Computation 34, 461-477 (2002)
    • (2002) J. Symbolic Computation , vol.34 , pp. 461-477
    • Xia, B.1    Yang, L.2
  • 21
    • 33846881998 scopus 로고    scopus 로고
    • Real Solution Isolation Using Interval Arithmetic
    • Xia, B., Zhang, T.: Real Solution Isolation Using Interval Arithmetic. Comput. Math. Appl. 52, 853-860 (2006)
    • (2006) Comput. Math. Appl , vol.52 , pp. 853-860
    • Xia, B.1    Zhang, T.2
  • 22
    • 0010223906 scopus 로고    scopus 로고
    • Recent advances on determining the number of real roots of parametric polynomials
    • Yang, L.: Recent advances on determining the number of real roots of parametric polynomials. J. Symbolic Computation 28, 225-242 (1999)
    • (1999) J. Symbolic Computation , vol.28 , pp. 225-242
    • Yang, L.1
  • 23
    • 0011564827 scopus 로고    scopus 로고
    • A complete algorithm for automated discovering of a class of inequality-type theorems
    • Yang, L., Hou, X., Xia, B.: A complete algorithm for automated discovering of a class of inequality-type theorems. Sci. in China (Ser. F) 44, 33-49 (2001)
    • (2001) Sci. in China (Ser. F) , vol.44 , pp. 33-49
    • Yang, L.1    Hou, X.2    Xia, B.3
  • 24
    • 1542787296 scopus 로고    scopus 로고
    • Yang, L., Hou, X., Zeng, Z.: A complete discrimination system for polynomials. Science in China (Ser. E) 39, 628-646 (1996)
    • Yang, L., Hou, X., Zeng, Z.: A complete discrimination system for polynomials. Science in China (Ser. E) 39, 628-646 (1996)
  • 25
    • 38049125265 scopus 로고    scopus 로고
    • Automated Deduction in Real Geometry
    • Chen, F, Wang, D, eds, World Scientific, Singapore
    • Yang, L., Xia, B.: Automated Deduction in Real Geometry. In: Chen, F., Wang, D. (eds.) Geometric Computation, pp. 248-298. World Scientific, Singapore (2004)
    • (2004) Geometric Computation , pp. 248-298
    • Yang, L.1    Xia, B.2
  • 26
    • 33749581656 scopus 로고    scopus 로고
    • Real solution classifications of a class of parametric semialgebraic systems
    • Yang, L., Xia, B.: Real solution classifications of a class of parametric semialgebraic systems. In: Proc. of Int'l Conf. on Algorithmic Algebra and Logic, pp. 281-289 (2005)
    • (2005) Proc. of Int'l Conf. on Algorithmic Algebra and Logic , pp. 281-289
    • Yang, L.1    Xia, B.2
  • 27
    • 38049138357 scopus 로고    scopus 로고
    • Program verification by using DISCOVERER
    • Zürich October 10-October 13, to appear
    • Yang, L., Zhan, N., Xia, B., Zhou, C.: Program verification by using DISCOVERER. In: Proc. VSTTE'05, Zürich (October 10-October 13, 2005) (to appear)
    • (2005) Proc. VSTTE'05
    • Yang, L.1    Zhan, N.2    Xia, B.3    Zhou, C.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.