Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Synthesizing inductive expertise
Information and Computation
Saving the phenomena: requirements that inductive inference machines not contradict known data
Information and Computation
Learning via queries to an oracle
COLT '89 Proceedings of the second annual workshop on Computational learning theory
On uniform learnability of language families
Information Processing Letters
On the role of procrastination in machine learning
Information and Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Synthesizing enumeration techniques for language learning
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Theoretical Computer Science - Special issue on algorithmic learning theory
Generalized notions of mind change complexity
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Ordinal mind change complexity of language identification
Theoretical Computer Science
Machine Inductive Inference and Language Identification
Proceedings of the 9th Colloquium on Automata, Languages and Programming
A Guided Tour Across the Boundaries of Learning Recursive Languages
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
Robust Learning with Infinite Additional Information
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Learning with Higher Order Additional Information
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Three Decades of Team Learning
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
Identifiability of Subspaces and Homomorphic Images of Zero-Reversible Languages
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
The Complexity of Universal Text-Learners
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
On the Learnability of Vector Spaces
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
On the learnability of vector spaces
Journal of Computer and System Sciences
Active Learning of Group-Structured Environments
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Topological Properties of Concept Spaces
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Learning Bounded Unions of Noetherian Closed Set Systems Via Characteristic Sets
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Commutative Regular Shuffle Closed Languages, Noetherian Property, and Learning Theory
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Theoretical Computer Science
Models of active learning in group-structured state spaces
Information and Computation
Topological properties of concept spaces (full version)
Information and Computation
Inferability of closed set systems from positive data
JSAI'06 Proceedings of the 20th annual conference on New frontiers in artificial intelligence
Computing characteristic sets of bounded unions of polynomial ideals
JSAI'07 Proceedings of the 2007 conference on New frontiers in artificial intelligence
Mind change complexity of inferring unbounded unions of pattern languages from positive data
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Inductive logic programming: yet another application of logic
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
Learning families of closed sets in matroids
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
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The present work investigates the learnability of classes of substructures of some algebraic structures: submonoids and subgroups of given groups, ideals of given commutative rings, subfields of given vector spaces. The learner sees all positive data but no negative one and converges to a program enumerating or computing the set to be learned. Besides semantical (BC) and syntactical (Ex) convergence also the more restrictive ordinal bounds on the number of mind changes are considered. The following is shown: (a) Learnability depends much on the amount of semantic knowledge given at the synthesis of the learner where this knowledge is represented by programs for the algebraic operations, codes for prominent elements of the algebraic structure (like 0 and 1 fields) and certain parameters (like the dimension of finite-dimensional vector spaces). For several natural examples, good knowledge of the semantics may enable to keep ordinal mind change bounds while restricted knowledge may either allow only BC-convergence or even not permit learnability at all. (b) The class of all ideals of a recursive ring is BC-learnable iff the ring is Noetherian. Furthermore, one has either only a BC-learner outputting enumerable indices or one can already get an Ex-learner converging to decision procedures and respecting an ordinal bound on the number of mind changes. The ring is Artinian iff the ideals can be Ex-learned with a constant bound on the number of mind changes, this constant is the length of the ring. Ex-learnability depends not only on the ring but also on the representation of the ring. Polynomial rings over the field of rationals with n variables have exactly the ordinal mind change bound in the standard representation. Similar results can be established for unars. Noetherian unars with one function can be learned with an ordinal mind change bound a&ohgr; for some a. Copyright 2001 Elsevier Science B.V. All rights reserved.