On the intractability of hilbert’s nullstellensatz and an algebraic version of "NP ≠ p?"

Duke Mathematical Journal

Volumn 81, Issue 1, 1995, Pages 47-54

  Shub, Michael ^a   Smale, Steve ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002040582     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-95-08105-8     Document Type: Article

References (9)

1. L. BLUM, M. SHUB, AND S. SMALE 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.
2. W. D. BROWNAWELL Bounds for the degrees in the Nullstellensatz, Ann. of Math. (2) 126 (1987), 577-591.
3. F. CUCKER, M. SHUB, AND S. SMALE Separation of complexity classes in Koiran’s weak model, to appear in Theoret. Comput. Sci.
4. J. HEINTZ "On the computational complexity of polynomials and bilinear mappings: A survey," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Comput. Sci., 356, Springer-Verlag, Berlin, 1989, 269-300.
5. J. HEINTZ AND J. MORGENSTERN On the intrinsic complexity of elimination theory, J. Complexity 9 (1993), 471-498.
6. W. DE MELO AND B. F. SVAITER The cost of computing integers, to appear in Proc. Amer. Math.Soc.
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" in From Topology to Computation: Proceedings of the Smalefast, ed. by M. W. HIRSCH, J. E. MARSDEN, and M. SHUB, Springer-Verlag, New York, 1993, 443-455.
9. L. G. VALIANT "Completeness classes in algebra," Conference Record of the Eleventh Annual ACM Symposium on Theory of Computing, ACM, New York, 1979, 249-261.