Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Elementary formal system as a unifying framework for language learning
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Types of monotonic language learning and their characterization
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learning elementary formal systems
Theoretical Computer Science
Short note: procedural semantics and negative information of elementary formal system
Journal of Logic Programming
Rich classes inferable from positive data
Information and Computation
Towards a mathematical theory of machine discovery from facts
Theoretical Computer Science - Special issue on algorithmic learning theory
Program synthesis in the presence of infinite number of inaccuracies
Journal of Computer and System Sciences
Theoretical Computer Science - Special issue on algorithmic learning theory
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)
Characterization of Finite Identification
AII '92 Proceedings of the International Workshop on Analogical and Inductive Inference
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
Inductive Inference of an Approximate Concept from Positive Data
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
On Approximately Identifying Concept Classes in the Limit
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Synthesizing Learners Tolerating Computable Noisy Data
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
Language Learning with a Neighbor System
DS '00 Proceedings of the Third International Conference on Discovery Science
Reflective Inductive Inference of Recursive Functions
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
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We consider inductive language learning and machine discovery from examples with some errors. In the present paper, the error or incorrectness we consider is the one described uniformly in terms of a distance over strings. Firstly, we introduce a notion of a recursively generable distance over strings, and for a language L, we define a k-neighbor language L驴 as a language obtained from L by (i) adding some strings not in L each of which is at most k distant from some string in L and by (ii) deleting some strings in L each of which is at most k distant from some string not in L. Then we define a k-neighbor system of a base language class as the collection of k-neighbor languages of languages in the class, and adopt it as a hypothesis space. We give formal definitions of k-neighbor (refutable) inferability, and discuss necessary and sufficient conditions on such kinds of inference.