Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Can finite samples detect singularities of real-valued functions?
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Towards a mathematical theory of machine discovery from facts
Theoretical Computer Science - Special issue on algorithmic learning theory
On the intrinsic complexity of learning
Information and Computation
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Inductive Inference: Theory and Methods
ACM Computing Surveys (CSUR)
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
Characterization Problems in the Theory of Inductive Inference
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
On the Classification of Computable Languages
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Inductive Inference Machines That Can Refute Hypothesis Spaces
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
Machine Discovery in the Presence of Incomplete or Ambiguous Data
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Reflecting and Self-Confident Inductive Inference Machines
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Reflecting Inductive Inference Machines and Its Improvement by Therapy
ALT '96 Proceedings of the 7th International Workshop on Algorithmic Learning Theory
Inductive Inference of Recursive Functions: Qualitative Theory
Baltic Computer Science, Selected Papers
One-sided error probabilistic inductive inference and reliable frequency identification
Information and Computation
Research in the theory of inductive inference by GDR mathematicians-A survey
Information Sciences: an International Journal
Reflective Inductive Inference of Recursive Functions
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
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Learning of recursive functions refutably means that for every recursive function, the learning machine has either to learn this function or to refute it, i.e., to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. All these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity; two of them do not contain function classes that are "most difficult" to learn, while the third one does. Moreover, we present characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general.For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. Then we derive hierarchies for refutable learning. Finally, we show that stricter refutability constraints cannot be traded for more liberal learning criteria.