Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Prudence and other conditions on formal language learning
Information and Computation
Regular Article: Open problems in “systems that learn”
Proceedings of the 30th IEEE symposium on Foundations of computer science
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
The Power of Pluralism for Automatic Program Synthesis
Journal of the ACM (JACM)
The Power of Vacillation in Language Learning
SIAM Journal on Computing
Machine Inductive Inference and Language Identification
Proceedings of the 9th Colloquium on Automata, Languages and Programming
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Results on memory-limited U-shaped learning
Information and Computation
Information and Computation
Resource Restricted Computability Theoretic Learning: Illustrative Topics and Problems
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
U-shaped, iterative, and iterative-with-counter learning
COLT'07 Proceedings of the 20th annual conference on Learning theory
Memory-limited u-shaped learning
COLT'06 Proceedings of the 19th annual conference on Learning Theory
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U-shaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether U-shaped learning behaviour may be necessary in the abstract mathematical setting of inductive inference, that is, in the computational learning theory following the framework of Gold. All notions considered are learning from text, that is, from positive data. Previous work showed that U-shaped learning behaviour is necessary for behaviourally correct learning but not for syntactically convergent, learning in the limit (= explanatory learning). The present paper establishes the necessity for the whole hierarchy of classes of vacillatory learning where a behaviourally correct learner has to satisfy the additional constraint that it vacillates in the limit between at most k grammars, where k ≥ 1. Non U-shaped vacillatory learning is shown to be restrictive: Every non U-shaped vacillatorily learnable class is already learnable in the limit. Furthermore, if vacillatory learning with the parameter k=2 is possible then non U-shaped behaviourally correct learning is also possible. But for k=3, surprisingly, there is a class witnessing that this implication fails.