Language identification in the limit is a formal model for inductive inference. It was introduced by E. Mark Gold in his paper with the same title . In this model, a learner is provided with presentation of some language. The learning is seen as an infinite process. Each time an element of the presentation is read the learner should provide a representation for the language. We say that a learner can identify in the limit a class of languages if given any presentation of any language in the class the learner will produce a finite number of wrong representations, and therefore converge on the correct representation in a finite number of steps, without however necessarily being able to announce its correctness since a counterexample to that representation could appear as an element arbitrarily long after.
Gold defined two types of presentations:
- Text (positive information): an enumeration of the language.
- Complete presentation (positive and negative information): an enumeration of all possible strings, each with a label indicating if the string belongs to the language or not.
Read more about Language Identification In The Limit: Learnability, Learnability Characterization, Language Classes Learnable in The Limit From Text, Language Classes Not Learnable in The Limit From Text, Sufficient Conditions For Learnability, Relations Between Concepts, Open Questions
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