Computability with low-dimensional dynamical systems
Theoretical Computer Science
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
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
Upper and Lower Bounds on Continuous-Time Computation
UMC '00 Proceedings of the Second International Conference on Unconventional Models of Computation
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)
The P ≠ NP conjecture in the context of real and complex analysis
Journal of Complexity
Can Newtonian systems, bounded in space, time, mass and energy compute all functions?
Theoretical Computer Science
Computability of analog networks
Theoretical Computer Science
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
A new conceptual framework for analog computation
Theoretical Computer Science
The New Promise of Analog Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
(Short) Survey of Real Hypercomputation
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)
The P≠NP conjecture in the context of real and complex analysis
Journal of Complexity
On the computational capabilities of several models
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
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
Solving analytic differential equations in polynomial time over unbounded domains
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
A network model of analogue computation over metric algebras
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
On the complexity of solving initial value problems
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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In this paper we show that Shannon's general purpose analog computer (GPAC) is equivalent to a particular class of recursive functions over the reals with the flavour of Kleene's classical recursive function theory.We first consider the GPAC and several of its extensions to show that all these models have drawbacks and we introduce an alternative continuous-time model of computation that solves these problems. We also show that this new model preserves all the significant relations involving the previous models (namely, the equivalence with the differentially algebraic functions).We then continue with the topic of recursive functions over the reals, and we show full connections between functions generated by the model introduced so far and a particular class of recursive functions over the reals.