Prudence and other conditions on formal language learning
Information and Computation
An easy priority-free proof of a theorem of Friedberg
Theoretical Computer Science
Polynomial-time inference of arbitrary pattern languages
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Incremental learning from positive data
Journal of Computer and System Sciences
Machine Inductive Inference and Language Identification
Proceedings of the 9th Colloquium on Automata, Languages and Programming
A Thesis in Inductive Inference
Proceedings of the 1st International Workshop on Nonmonotonic and Inductive Logic
Results on memory-limited U-shaped learning
Information and Computation
Learning in Friedberg numberings
Information and Computation
Topological properties of concept spaces (full version)
Information and Computation
Iterative learning of simple external contextual languages
Theoretical Computer Science
Incremental learning with temporary memory
Theoretical Computer Science
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
| Hi-index | 5.23 |
Iterative learning is a model of language learning from positive data, due to Wiehagen. When compared to a learner in Gold's original model of language learning from positive data, an iterative learner can be thought of as memory-limited. However, an iterative learner can memorize some input elements by coding them into the syntax of its hypotheses. A main concern of this paper is: to what extent are such coding tricks necessary? One means of preventing some such coding tricks is to require that the hypothesis space used be free of redundancy, i.e., that it be 1-1. In this context, we make the following contributions. By extending a result of Lange and Zeugmann, we show that many interesting and non-trivial classes of languages can be iteratively identified using a Friedberg numbering as the hypothesis space. (Recall that a Friedberg numbering is a 1-1 effective numbering of all computably enumerable sets.) An example of such a class is the class of pattern languages over an arbitrary alphabet. On the other hand, we show that there exists an iteratively identifiable class of languages that cannot be iteratively identified using any 1-1 effective numbering as the hypothesis space. We also consider an iterative-like learning model in which the computational component of the learner is modeled as an enumeration operator, as opposed to a partial computable function. In this new model, there are no hypotheses, and, thus, no syntax in which the learner can encode what elements it has or has not yet seen. We show that there exists a class of languages that can be identified under this new model, but that cannot be iteratively identified. On the other hand, we show that there exists a class of languages that cannot be identified under this new model, but that can be iteratively identified using a Friedberg numbering as the hypothesis space.