A guided tour across the boundaries of learning recursive languages

“…⊂ LimTxt r.e. , as witnessed by the indexable class used in [19] to separate LimTxt-learnable indexable classes from ConsvTxt-learnable indexable classes. Another often studied version of Gold-style language learning is behaviourally correct learning [6]: If C is a class of r.e.…”

Section: Gold-style Language Learningmentioning

confidence: 99%

“…4 Recently, the combination of these two approaches [11,12] as well as the common features of learners in either model [14,15] have gained interest in the learning theory community. [14,15] contributes a systematic analysis of common features of both approaches, thereby focussing on the identification of formal languages, ranging over indexable classes of recursive languages, as target concepts, see [2,13,19]. Characterising different types of Gold-style language learning in terms of query learning has pointed out correspondences between the two models.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gold-Style and Query Learning Under Various Constraints on the Target Class

Jain

Lange

Zilles

2005

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. In language learning, strong relationships between Gold-style models and query models have recently been observed: in some quite general setting Gold-style learners can be replaced by query learners and vice versa, without loss of learning capabilities. These 'equalities' hold in the context of learning indexable classes of recursive languages. Former studies on Gold-style learning of such indexable classes have shown that, in many settings, the enumerability of the target class and the recursiveness of its languages are crucial for learnability. Moreover, studying query learning, non-indexable classes have been mainly neglected up to now. So it is conceivable that the recently observed relations between Gold-style and query learning are not due to common structures in the learning processes in both models, but rather to the enumerability of the target classes or the recursiveness of their languages. In this paper, the analysis is lifted onto the context of learning arbitrary classes of r.e. languages. Still, strong relationships between the approaches of Gold-style and query learning are proven, but there are significant changes to the former results. Though in many cases learners of one type can still be replaced by learners of the other type, in general this does not remain valid vice versa. All results hold even for learning classes of recursive languages, which indicates that the recursiveness of the languages is not crucial for the former 'equality' results. Thus we analyse how constraints on the algorithmic structure of the target class affect the relations between two approaches to language learning.

show abstract

“…In his pioneering paper, Gold [7] gave precise definitions of the concepts "evidence," "stabilization," and "accuracy" resulting in the model of learning in the limit. During the last decades, Gold-style formal language learning has attracted a lot of attention by computer scientists (cf., e.g., Osherson, Stob and Weinstein [14], Jain et al [10] as well as Zeugmann and Lange [22], and the references therein). Most of the work done in the field has been aimed at the following goals: showing what general collections of language classes are learnable, characterizing those collections of language classes that can be learned, studying the impact of several postulates on the behavior of learners to their learning power, and dealing with the influence of various parameters to the efficiency of learning.…”

Section: Introductionmentioning

confidence: 99%