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
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Characterizing Computable Analysis with Differential Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
ACM Transactions on Computational Logic (TOCL)
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
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Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955] as an approach for investigating computation over the real numbers. It is based on enhancing the Turing machine model by introducing oracles that allow the machine to access finitary portions of the real infinite objects. Classes of computable real functions have been extensively studied as well as complexity-theoretic classes of functions restricted to compact domains. However, much less have been done regarding complexity of arbitrary real functions. In this article we give a definition of polynomial time computability of arbitrary real functions. Then we present two main applications based on that definition. The first one, which has already been published, concerns the relationships between polynomial time real computability and the corresponding notion over continuous rational functions. The second application, which is a new contribution to this article, concerns the construction of a function algebra that captures polynomial time real computability.