Classes of Grzegorczyk-computable real numbers
Classes of Grzegorczyk-computable real numbers
Complexity theory of real functions
Complexity theory of real functions
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Computable analysis: an introduction
Computable analysis: an introduction
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
Subclasses of Coputable Real Valued Functions
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
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
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)
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
Characterizing Computable Analysis with Differential Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
ACM Transactions on Computational Logic (TOCL)
The P≠NP conjecture in the context of real and complex analysis
Journal of Complexity
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
Real recursive functions and real extensions of recursive functions
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
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The theory of analog computation aims at modeling computational systems that evolve in a continuous space. Unlike the situation with the discrete setting there is no unified theory of analog computation. There are several proposed theories, some of them seem quite orthogonal. Some theories can be considered as generalizations of the Turing machine theory and classical recursion theory. Among such are recursive analysis and Moore's class of recursive real functions. Recursive analysis was introduced by Turing (Proc Lond Math Soc 2(42):230---265, 1936), Grzegorczyk (Fundam Math 42:168---202, 1955), and Lacombe (Compt Rend l'Acad Sci Paris 241:151---153, 1955). Real computation in this context is viewed as effective (in the sense of Turing machine theory) convergence of sequences of rational numbers. In 1996 Moore introduced a function algebra that captures his notion of real computation; it consists of some basic functions and their closure under composition, integration and zero-finding. Though this class is inherently unphysical, much work have been directed at stratifying, restricting, and comparing it with other theories of real computation such as recursive analysis and the GPAC. In this article we give a detailed exposition of recursive analysis and Moore's class and the relationships between them.