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Complexity theory of real functions
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Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Networks of spiking neurons: the third generation of neural network models
Transactions of the Society for Computer Simulation International - Special issue: simulation methodology in transportation systems
Computable analysis: an introduction
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Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
Analog computers and recursive functions over the reals
Journal of Complexity
Elementarily computable functions over the real numbers and R-sub-recursive functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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
Polynomial time computation in the context of recursive analysis
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
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
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The functions of Computable Analysis are defined by enhancing the capacities of normal Turing Machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as Real Recursive Functions. Bournez and Hainry 2006 [Bournez, O. and E. Hainry, Recursive analysis characterized as a class of real recursive functions, Fundamenta Informaticae 74 (2006), pp. 409-433] used a function algebra to characterize the twice continuously differentiable functions of Computable Analysis, restricted to certain compact domains. In a similar model, Shannon's General Purpose Analog Computer, Bournez et. al. 2007 [Bournez, O., M. L. Campagnolo, D. S. Graca and E. Hainry, Polynomial differential equations compute all real computable functions on computable compact intervals, Journal of Complexity 23 (2007), pp. 317-335] also characterize the functions of Computable Analysis. We combine the results of [Bournez, O. and E. Hainry, Recursive analysis characterized as a class of real recursive functions, Fundamenta Informaticae 74 (2006), pp. 409-433] and Graca et. al. [Graca, D. S., N. Zhong and J. Buescu, Computability, noncomputability and undecidability of maximal intervals of IVPs, Transactions of the American Mathematical Society (2007), to appear], to show that a different function algebra also yields Computable Analysis. We believe that our function algebra is an improvement due to its simple definition and because the operations in our algebra are less obviously designed to mimic the operations in the usual definition of the recursive functions using the primitive recursion and minimization operators.