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Volumn 15, Issue 2, 1999, Pages 227-238

The Real Dimension Problem Is NPR-Complete

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EID: 0008807053     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1999.0502     Document Type: Article
Times cited : (28)

References (19)
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    • Basu, S.1    Pollack, R.2    Roy, M.-F.3
  • 4
    • 84968516134 scopus 로고
    • On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines
    • Blum L., Shub M., Smale S. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bull. Amer. Math. Soc. 21:1989;1-46.
    • (1989) Bull. Amer. Math. Soc. , vol.21 , pp. 1-46
    • Blum, L.1    Shub, M.2    Smale, S.3
  • 7
    • 0004526137 scopus 로고    scopus 로고
    • Saturation and stability in the theory of computation over the reals
    • Technical Report, 1997/3, Institut Girard Desargues, Université Claude Bernard Lyon I, to appear
    • O. Chapuis, and, P. Koiran, Saturation and stability in the theory of computation over the reals, Technical Report, 1997/3, Institut Girard Desargues, Université Claude Bernard Lyon I, 1997, Ann. Pure Appl. Logic, to appear.
    • (1997) Ann. Pure Appl. Logic
    • Chapuis, O.1    Koiran, P.2
  • 8
    • 0030187917 scopus 로고    scopus 로고
    • Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic
    • Chistov A. Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic. J. Symbolic Comput. 22:1996;1-25.
    • (1996) J. Symbolic Comput. , vol.22 , pp. 1-25
    • Chistov, A.1
  • 9
    • 84971574419 scopus 로고
    • On the complexity of some problems for the Blum, Shub and Smale model
    • New York/Berlin: Springer-Verlag. p. 117-129
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    • (1992) Proceedings of Latin'92 Lecture Notes in Computer Science , vol.583
    • Cucker, F.1    Roselló, F.2
  • 10
    • 0000750175 scopus 로고
    • Algorithmes-disons rapides-pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles
    • T. Mora, & C. Traverso. Basel: Birkhäuser
    • Giusti M., Heintz J. Algorithmes-disons rapides-pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles. Mora T., Traverso C. Effective Methods in Algebraic Geometry (MEGA'90). Progress in Mathematics. 94:1991;169-194 Birkhäuser, Basel.
    • (1991) Effective Methods in Algebraic Geometry (MEGA'90). Progress in Mathematics , vol.94 , pp. 169-194
    • Giusti, M.1    Heintz, J.2
  • 11
    • 0000936391 scopus 로고
    • La détermination des points isolés et la dimension d'une variété algébrique peut se faire en temps polynomial
    • Cambridge: Cambridge Univ. Press. p. 216-256
    • Giusti M., Heintz J. La détermination des points isolés et la dimension d'une variété algébrique peut se faire en temps polynomial. Computational Algebraic Geometry and Commutative Algebra (Cortono, 1991). Sympos. Math. 34:1993;Cambridge Univ. Press, Cambridge. p. 216-256.
    • (1993) Computational Algebraic Geometry and Commutative Algebra (Cortono, 1991) Sympos. Math. , vol.34
    • Giusti, M.1    Heintz, J.2
  • 12
    • 0031094141 scopus 로고    scopus 로고
    • Elimination of constants from machines over algebraically closed fields
    • Koiran P. Elimination of constants from machines over algebraically closed fields. J. Complexity. 13:1997;65-82.
    • (1997) J. Complexity , vol.13 , pp. 65-82
    • Koiran, P.1
  • 17
    • 0001572510 scopus 로고
    • On the computational complexity and geometry of the first-order theory of the reals, parts I, II, III
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    • (1992) J. Symbolic Comput. , vol.13 , pp. 255-352
    • Renegar, J.1
  • 18
    • 0000155802 scopus 로고
    • Polynomials with rational coefficients which are hard to compute
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    • Strassen, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.