Computational geometry: an introduction
Computational geometry: an introduction
Complexity theory of real functions
Complexity theory of real functions
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Recursive characterization of computable real-valued functions and relations
Theoretical Computer Science - Special issue on real numbers and computers
Complexity and real computation
Complexity and real computation
Networks of spiking neurons: the third generation of neural network models
Transactions of the Society for Computer Simulation International - Special issue: simulation methodology in transportation systems
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Feasible real random access machines
Journal of Complexity
Computable analysis: an introduction
Computable analysis: an introduction
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
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)
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Electronic Notes in Theoretical Computer Science (ENTCS)
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
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The functions of computable analysis are defined by enhancing normal Turing machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as real recursive functions. Since there are numerous incompatible models of computation over the reals, it is interesting to find that the two very different models we consider can be set up to yield exactly the same functions. Bournez and Hainry used a function algebra to characterize computable analysis, restricted to the twice continuously differentiable functions with compact domains. In our earlier paper, we found a different (and apparently more natural) function algebra that also yields computable analysis, with the same restriction. In this paper we improve earlier work, finding three function algebras characterizing computable analysis, removing the restriction to twice continuously differentiable functions and allowing unbounded domains. One of these function algebras is built upon the widely studied real primitive recursive functions. Furthermore, the proof of this paper uses our previously developed method of approximation, whose applicability is further evidenced by this paper.