On the Complexity of Hilbert's 17th Problem
暂无分享,去创建一个
[1] D. Hilbert. Über die Darstellung definiter Formen als Summe von Formenquadraten , 1888 .
[2] D. Hilbert. Über ternäre definite Formen , 1893 .
[3] G. M.. Grundlagen der Geometrie , 1909, Nature.
[4] E. Artin. Über die Zerlegung definiter Funktionen in Quadrate , 1927 .
[5] A. Pfister. Zur Darstellung definiter Funktionen als Summe von Quadraten , 1967 .
[6] Stephen A. Cook,et al. The complexity of theorem-proving procedures , 1971, STOC.
[7] K. Ramachandra,et al. Vermeidung von Divisionen. , 1973 .
[8] Miss A.O. Penney. (b) , 1974, The New Yale Book of Quotations.
[9] G. Stengle. A nullstellensatz and a positivstellensatz in semialgebraic geometry , 1974 .
[10] F. Browder. Mathematical developments arising from Hilbert problems , 1976 .
[11] Irving Kaplansky. Review: Felix E. Browder, Mathematical developments arising from Hilbert problems , 1977 .
[12] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .
[13] B. Reznick,et al. The Pythagoras number of some affine algebras and local algebras. , 1982 .
[14] Oscar H. Ibarra,et al. Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs , 1983, JACM.
[15] Stathis Zachos,et al. Does co-NP Have Short Interactive Proofs? , 1987, Inf. Process. Lett..
[16] Erich Kaltofen,et al. Greatest common divisors of polynomials given by straight-line programs , 1988, JACM.
[17] Marie-Françoise Roy,et al. Real algebraic geometry , 1992 .
[18] B. Reznick. Uniform denominators in Hilbert's seventeenth problem , 1995 .
[19] Olga Taussky-Todd. SOME CONCRETE ASPECTS OF HILBERT'S 17TH PROBLEM , 1996 .
[20] Sanjeev Arora,et al. Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.
[21] Marie-Françoise Roy,et al. Witt Rings in Real Algebraic Geometry , 1998 .
[22] Charles N. Delzell,et al. Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra , 2001 .
[23] B. Reznick,et al. A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra , 2001 .
[24] Grigoriy Blekherman. There are significantly more nonegative polynomials than sums of squares , 2003, math/0309130.
[25] Rüdger Thiele,et al. Hilbert's Twenty-Fourth Problem , 2002, Journal of Automated Reasoning.