that language.If a computer program for the learner's role would exist that was able to successfully learn each regular language, that class of languages would be identifiable in the limit. Gold has shown that this is not the case. A particular learning algorithm always guessing L to be just the union of all strings seen so far:If L is a finite language, the learner will eventually guess it correctly, however, without being able to tell when. Although the guess didn't change during step 3 to 6, the learner couldn't be sure to be correct.Gold has shown that the class of finite languages is identifiable in the limit, however, this class is neither finitely nor fixed-time identifiable. Learning from complete presentation by telling:In each step, the teacher gives a string and tells whether it belongs to L () or not (). Each possible string is eventually classified in this way by the teacher. Learning from complete presentation by request:The learner gives a query string, the teacher tells whether it belongs to L () or not (); the learner then gives a guess for L, followed by the next query string. In this example, the learner happens to query in each step just the same string as given by the teacher in example 3.In general, Gold has shown that each language class identifiable in the request-presentation setting is also identifiable in the telling-presentation setting, since the learner, instead of querying a string, just needs to wait until it is eventually given by the teacher. Gold's theorem More formally, a language is a nonempty set, and its elements are called sentences. a language family is a set of languages. a language-learning environment for a language is a stream of sentences from , such that each sentence in appears at least once. a language learner is a function that sends a list of sentences to a language. This is interpreted as saying that, after seeing sentences in that order, the language learner guesses that the language that produces the sentences should be . Note that the learner is not obliged to be correct — it could very well guess a language that does not even contain . a language learner learns a language in environment if the learner always guesses after seeing enough examples from the environment. a language learner learns a language if it learns in any environment for . a language family