Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Complexity and real computation
Complexity and real computation
Achilles and the Tortoise climbing up the hyper-arithmetical hierarchy
Theoretical Computer Science - Special issue on real numbers and computers
Achilles and the tortoise climbing up the arithmetical hierarchy
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Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
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U.S. Technological Enthusiasm and British Technological Skepticism in the Age of the Analog Brain
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An analog characterization of the Grzegorczyk hierarchy
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Subclasses of Coputable Real Valued Functions
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Theoretical Computer Science
Perturbed Turing Machines and Hybrid Systems
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Analog computers and recursive functions over the reals
Journal of Complexity
Real recursive functions and their hierarchy
Journal of Complexity
Real recursive functions and real extensions of recursive functions
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
The computational power of continuous dynamic systems
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
The Methods of Approximation and Lifting in Real Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
The New Promise of Analog Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Characterizing Computable Analysis with Differential Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
Using approximation to relate computational classes over the reals
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
A characterization of computable analysis on unbounded domains using differential equations
Information and Computation
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: we prove that they correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema.We generalize this result to all higher levels of the Grzegorczyk Hierarchy.This paper improves several previous partial characterizations and has a dual interest: • Concerning recursive analysis, our results provide machine-independent characterizations of natural classes of computable functions over the real numbers, allowing to define these classes without usual considerations on higher-order (type 2) Turing machines. • Concerning analog models, our results provide a characterization of the power of a natural class of analog models over the real numbers and provide new insights for understanding the relations between several analog computational models.