Blum, L., M. Shub, S. Smale , On a Theory of Computation and Complexity over the Real Numbers; NP Completeness, Recursive Functions and Universal Machines, Bull. Amer. Math. Soc. (New Series) Vol. 21 (1989) 1-46. Home/Search Document Not in Database Summary Related Articles Check |
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The Complexity of Accurate Floating Point Computation - Demmel (2002) (Correct)
....the outputs are in fact accurately determined by the inputs, in the sense that small relative changes in the inputs cause small relative changes in the outputs. We make this conjecture more precise in section 3 below. There are many ways to formulate the search for e#cient and accurate algorithms [6, 4, 19, 3, 13, 18, 16]. Our approach di#ers in several ways. In contrast to either conventional floating point error analysis [13] or the model in [6] we ask that even the tiniest results have correct leading digits, and that zero be exact. In [6] the model of arithmetic allows a tiny absolute error in each operation, ....
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. AMS Bulletin (New Series), 21(1):1--46, July 1989.
Recursion Theory on the Reals and Continuous-time Computation - Moore (1995) (20 citations) (Correct)
....into a compact subset of itself. This allows us to construct an operator j, which searches over all of R in finite time , rendering the Halting Problem decidable. 2 Comparison with Other Models of Computation on the Reals The best known recent model of analog computation is Blum Shub Smale s [4]. They define flowchart machines whose states are finite dimensional vectors of real or complex numbers, whose elementary operations are rational functions, and which can branch on polynomial inequalities. Our definition differs from this one in several ways. First, if we re going to discuss ....
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.
On the Mortality Problem for Matrices of Low Dimensions - Bournez, Branicky (Correct)
.... Instance: a nite set F of d d matrices with entries in K (resp. a set F of m d d matrices with entries in K) The main contributions of the paper are: An undecidability result, already in the case of only two 2 2 matrices, for K = R in the Blum Shub Smale model of computation [5]. A decidability result for two 2 2 matrices, in the case K = Q for the Turing model of computation. For arbitrary jF j = m, the question remains open. Reducibility relations between the mortality problem and other problems in the literature. 2 Links between dimension and number of ....
.... machine model studied in recursive analysis (e.g. see [26] However, this model does not meet our needs because one cannot decide whether a real number is equal to zero in this model [26] Another approach is to use the Turing machine model for real numbers proposed by Blum, Shub, and Smale in [4, 5]. Roughly speaking, a BSS machine is an extended Random Access Machine [10] that treats real numbers as basic entities; namely a BSS machine contains an unbounded number of real registers x 1 ; xn ; each of which can hold one real number in unbounded precision. Moreover, a ....
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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. Bulletin of the American Mathematical Society, 21(1):1-46, July 1989. 15
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Blum, L., M. Shub, S. Smale , On a Theory of Computation and Complexity over the Real Numbers; NP Completeness, Recursive Functions and Universal Machines, Bull. Amer. Math. Soc. (New Series) Vol. 21 (1989) 1-46.
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Blum, L., Shub, M., and Smale, S. On a theory of computation and complexity over the real numbers: Np-compleness, recursive functions and universal machines. Bulletin of the American Mathematical Society 21, 1 (July 1989), 146.
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L. Blum, M. Shub, 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
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L. Blum, M. Shub, 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.
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L. Blum, M. Shub, S. Smale, On a Theory of Computation and Complexity over the Real Numbers: NP-completeness, Recursive Functions, and Universal Machines. Bull. Amer. Math. Soc., 1989, Vol. 21, No. 1, pp. 1--46.
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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. Bulletin of the Amer. Math. Soc., 21:1--46, 1989.
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L. Blum, M. Shub & S. Smale, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bull. of the AMS, 21, N 1, 1--46 (1989).
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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. Bulletin of the American Mathematical Society, 21(1):1--46, July 1989.
A Survey on Real Structural Complexity Theory - Meer, Michaux (1997) (7 citations) (Correct)
No context found.
L. Blum, M. Shub, 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.
A Survey on Real Structural Complexity Theory - Meer, Michaux (1997) (7 citations) (Correct)
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L. Blum, A Theory of Computation and Complexity over the real numbers, Proceedings of the International Congress of Mathematicians Kyoto 1990.
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