Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Handbook of theoretical computer science (vol. B)
Complexity theory of real functions
Complexity theory of real functions
Relatively recursive reals and real functions
Theoretical Computer Science - Special issue on real numbers and computers
Computable analysis: an introduction
Computable analysis: an introduction
Topological properties of real number representations
Theoretical Computer Science
Computability theory of generalized functions
Journal of the ACM (JACM)
Revising Type-2 Computation and Degrees of Discontinuity
Electronic Notes in Theoretical Computer Science (ENTCS)
(Short) Survey of Real Hypercomputation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Computability of Analytic Functions with Analytic Machines
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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The sometimes so-called Main Theorem of Recursive Analysis implies that any computable real function is necessarily continuous. We consider three relaxations of this common notion of real computability for the purpose of treating also discontinuous functions f: ℝ→ℝ: non-deterministic computation; relativized computation, specifically given access to oracles like ∅′ or ∅″; encoding input xεℝ and/or output y = f(x) in weaker ways according to the Real Arithmetic Hierarchy. It turns out that, among these approaches, only the first one provides the required power.