Regular Article: The Extended Analog Computer
Advances in Applied Mathematics
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Achilles and the tortoise climbing up the arithmetical hierarchy
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Computable analysis: an introduction
Computable analysis: an introduction
U.S. Technological Enthusiasm and British Technological Skepticism in the Age of the Analog Brain
IEEE Annals of the History of Computing
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
µ-recursion and infinite limits
Theoretical Computer Science
Infinite limits and R-recursive functions
Acta Cybernetica
Analog computers and recursive functions over the reals
Journal of Complexity
Real recursive functions and their hierarchy
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)
Real recursive functions and real extensions of recursive functions
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)
Differential equations, infinite limits and real recursive functions
ACC'08 Proceedings of the WSEAS International Conference on Applied Computing Conference
Distributed Learning of Wardrop Equilibria
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Characterizing Computable Analysis with Differential Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
ACM Transactions on Computational Logic (TOCL)
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
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
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Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimalization and limit schema.