On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “$NP\not=P$?”
Michael Shub and Steve Smale
Source: Duke Math. J. Volume 81, Number 1
(1995), 47-54.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245460
Mathematical Reviews number (MathSciNet): MR1381969
Zentralblatt MATH identifier: 0882.03040
Digital Object Identifier: doi:10.1215/S0012-7094-95-08105-8
References
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Mathematical Reviews (MathSciNet): MR90a:68022
Zentralblatt MATH: 0681.03020
Digital Object Identifier: doi:10.1090/S0273-0979-1989-15750-9
Project Euclid: euclid.bams/1183555121
[2] W. D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. (2) 126 (1987), no. 3, 577–591.
Mathematical Reviews (MathSciNet): MR89b:12001
Zentralblatt MATH: 0641.14001
Digital Object Identifier: doi:10.2307/1971361
JSTOR: links.jstor.org
[3] F. Cucker, M. Shub, and S. Smale, Separation of complexity classes in Koiran's weak model, to appear in Theoret. Comput. Sci.
Mathematical Reviews (MathSciNet): MR1294421
Zentralblatt MATH: 0819.68053
Digital Object Identifier: doi:10.1016/0304-3975(94)00069-7
[4] J. Heintz, On the computational complexity of polynomials and bilinear mappings: A survey, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Menorca, 1987), Lecture Notes in Comput. Sci., vol. 356, Springer-Verlag, Berlin, 1989, pp. 269–300.
Mathematical Reviews (MathSciNet): MR1008543
Zentralblatt MATH: 0678.68036
[5] J. Heintz and J. Morgenstern, On the intrinsic complexity of elimination theory, J. Complexity 9 (1993), no. 4, 471–498.
Mathematical Reviews (MathSciNet): MR94k:12012
Zentralblatt MATH: 0835.68054
Digital Object Identifier: doi:10.1006/jcom.1993.1031
[6] W. de Melo and B. F. Svaiter, The cost of computing integers, to appear in Proc. Amer. Math. Soc.
Mathematical Reviews (MathSciNet): MR1307510
Zentralblatt MATH: 0851.11054
Digital Object Identifier: doi:10.1090/S0002-9939-96-03173-5
JSTOR: links.jstor.org
[7] C. G. Moreira, On asymptotic estimates for arithmetic cost functions, to appear.
[8] M. Shub, Some remarks on Bezout's Theorem and complexity theory, From Topology to Computation: Proceedings of the Smalefest (Berkeley, CA, 1990) eds. M. W. Hirsch, J. E. Marsden, and M. Shub, Springer-Verlag, New York, 1993, pp. 443–455.
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[9] L. G. Valiant, Completeness classes in algebra, Conference Record of the Eleventh Annual ACM Symposium on Theory of Computing (Atlanta, Ga., 1979), ACM, New York, 1979, pp. 249–261.
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