Titlebook: Complexity and Real Computation; Lenore Blum,Felipe Cucker,Steve Smale Textbook 1998 Springer Science+Business Media New York 1998 algorit

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https://doi.org/10.1007/978-1-4615-2476-2ex polynomial equations in .-unknowns. It is the goal of this chapter to prove Bézout’s Theorem. In Chapter 16 we use Bézout’s Theorem as a tool to derive geometric upper bounds on the number of connected components of semi-algebraic sets and complexity-theoretic lower bounds on some problems such a

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Springer Series in Solid-State Sciences Section 15.1 we show that inputs for rational machines can be supposed to be given by pairs of integers without substantially altering the complexity of the considered problem. In Section 15.2 we define an auxiliary problem which is a modification of the linear programming optimization problem and

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Lenore Blum,Felipe Cucker,Steve SmaleUnique work on this core topic * Written by internationally recognised specialists in mathematics and computing * Provides the basics for numerous practical industrial applications, e.g. AI, robotics,

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Anne Bosch,Michiel Steyaert,Willy SansenWe begin the development of our theory of computation with the definition of a . over a ring. Although it is necessary to define a . to be a more general object in order to fully develop a uniform theory —in particular with regard to complexity issues— a great deal can already be gleaned from the finite-dimensional case.