Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Subrecursive programming systems: complexity & succinctness
Subrecursive programming systems: complexity & succinctness
Regular Article: Open problems in “systems that learn”
Proceedings of the 30th IEEE symposium on Foundations of computer science
Language learning from texts: mindchanges, limited memory, and monotonicity
Information and Computation
On the impact of forgetting on learning machines
Journal of the ACM (JACM)
Incremental learning from positive data
Journal of Computer and System Sciences
Incremental concept learning for bounded data mining
Information and Computation
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
Results on memory-limited U-shaped learning
Information and Computation
Information and Computation
Non-U-shaped vacillatory and team learning
Journal of Computer and System Sciences
Incremental learning with temporary memory
Theoretical Computer Science
Iterative learning from texts and counterexamples using additional information
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Optimal language learning from positive data
Information and Computation
Memory-limited non-U-shaped learning with solved open problems
Theoretical Computer Science
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A U-shape occurs when a learner first learns, then unlearns, and, finally, relearns, some target concept. Within the framework of Inductive Inference, previous results have shown, for example, that U-shapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning. This paper solves the following two problems regarding non-U-shaped learning posed in the prior literature. First, it is shown that there are classes learnable with three memory states that are not learnable non-U-shapedly with any finite number of memory states. This result is surprising, as for learning with one or two memory states, U-shapes are known to be unnecessary. Secondly, it is shown that there is a class learnable memorylessly with a single feedback query such that this class is not learnable non-U-shapedly memorylessly with any finite number of feedback queries. This result is complemented by the result that any class of infinite languages learnable memorylessly with finitely many feedback queries is so learnable without U-shapes - in fact, all classes of infinite languages learnable with complete memory are learnable memorylessly with finitely many feedback queries and without U-shapes. On the other hand, we show that there is a class of infinite languages learnable memorylessly with a single feedback query, which is not learnable without U-shapes by any particular bounded number of feedback queries.