Some mathematical limitations of the general-purpose analog computer
Advances in Applied Mathematics
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
Small universal Turing machines
Theoretical Computer Science - Special issue on universal machines and computations
Complexity and real computation
Complexity and real computation
Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
Theoretical Computer Science - Special issue on computability and complexity in analysis
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
IEEE Annals of the History of Computing
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
The Complexity of Real Recursive Functions
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
µ-recursion and infinite limits
Theoretical Computer Science
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)
The P ≠ NP conjecture in the context of real and complex analysis
Journal of Complexity
Computability of analog networks
Theoretical Computer Science
First and Second Order Recursion on Abstract Data Types
Fundamenta Informaticae
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
Differential equations, infinite limits and real recursive functions
ACC'08 Proceedings of the WSEAS International Conference on Applied Computing Conference
The New Promise of Analog Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
ACM Transactions on Computational Logic (TOCL)
The P≠NP conjecture in the context of real and complex analysis
Journal of Complexity
Using approximation to relate computational classes over the reals
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
How to compare the power of computational models
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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
Real Recursive Functions and Baire Classes
Fundamenta Informaticae
First and Second Order Recursion on Abstract Data Types
Fundamenta Informaticae
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In the last years, recursive functions over the reals (Theoret. Comput. Sci. 162 (1996) 23) have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes (Unconventional Models of Computation, UMC 2002, Lecture Notes in Computer Science, Vol. 2509, Springer, Berlin, pp. 1-14). However, one of the operators introduced in the seminal paper by Moore (1996), the minimalization operator, has not been considered: (a) although differential recursion (the analog counterpart of classical recurrence) is, in some extent, directly implementable in the General Purpose Analog Computer of Claude Shannon, analog minimalization is far from physical realizability, and (b) analog minimalization was borrowed from classical recursion theory and does not fit well the analytic realm of analog computation. In this paper, we show that a most natural operator captured from analysis--the operator of taking a limit--can be used properly to enhance the theory of recursion over the reals, providing good solutions to puzzling problems raised by the original model.