Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Handbook of theoretical computer science (vol. B)
Relatively recursive reals and real functions
Theoretical Computer Science - Special issue on real numbers and computers
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computability on continuous, lower semi-continuous and upper semi-continuous real functions
Theoretical Computer Science
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)
Algorithmic complexity of recursive and inductive algorithms
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Real Hypercomputation and Continuity
Theory of Computing Systems
Admissible representations in computable analysis
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Computability and continuity on the real arithmetic hierarchy and the power of type-2 nondeterminism
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS2000), Brattka (MLQ2005), and Ziegler (ToCS2006) have considered different relaxed notions of computability to cover also discontinuous functions. The present work compares and unifies these approaches. This is based on the concept of the jump of a representation: both a TTE-counterpart to the well known recursion-theoretic jump on Kleene's Arithmetical Hierarchy of hypercomputation: and a formalization of revising computation in the sense of Shoenfield. We also consider Markov and Banach/Mazur oracle-computation of discontinuous functions and characterize the computational power of Type-2 nondeterminism to coincide with the first level of the Analytical Hierarchy.