A survey of transcendentally transcendental functions
American Mathematical Monthly
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
Computable analysis: an introduction
Analog computers and recursive functions over the reals
Journal of Complexity
Real recursive functions and their hierarchy
Journal of Complexity
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Computability of analog networks
Theoretical Computer Science
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)
Abstract Geometrical Computation and Computable Analysis
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
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
On the complexity of solving initial value problems
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
| Hi-index | 0.00 |
In the last decade, there have been several attempts to understand the relations between the many models of analog computation. Unfortunately, most models are not equivalent. Euler's Gamma function, which is computable according to computable analysis, but that cannot be generated by Shannon's General Purpose Analog Computer (GPAC), has often been used to argue that the GPAC is less powerful than digital computation. However, when computability with GPACs is not restricted to real-time generation of functions, it has been shown recently that Gamma becomes computable by a GPAC. Here we extend this result by showing that, in an appropriate framework, the GPAC and computable analysis are actually equivalent from the computability point of view, at least in compact intervals. Since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions over compact intervals can be defined by such models.