Recently, rich subclasses of elementary formal systems (EFS) have been shown to be identifiable in the limit from only positive data. Examples of these classes are Angluin’s pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by length-bounded elementary formal systems studied by Shinohara. The present paper employs two distinct bodies of abstract studies in the inductive inference literature to analyze the learnability of these concrete classes. The first approach, introduced by Freivalds and Smith, uses constructive ordinals to bound the number of mind changes. ω denotes the first limit ordinal. An ordinal mind change bound of ω means that identification can be carried out by a learner that after examining some element(s) of the language announces an upper bound on the number of mind changes it will make before converging; a bound of ω · 2 means that the learner reserves the right to revise this upper bound once; a bound of ω · 3 means the learner reserves the right to revise this upper bound twice, and so on. A bound of ω 2 means that identification can be carried out by a learner that announces an upper bound on the number of times it may revise its conjectured upper bound on the number of mind changes. It is shown in the present paper that the ordinal mind change complexity for identification of languages formed by unions of up to n pattern languages is ω n. It is

Abstract. It is investigated for which choice of a parameter q, denoting the number of contexts, the class of simple external contextual languages is iteratively learnable. On one hand, the class admits, for all values of q, polynomial time learnability provided an adequate choice of the hypothesis space is given. On the other hand, additional constraints like consistency and conservativeness or the use of a one-one hypothesis space changes the picture — iterative learning limits the long term memory of the learner to the current hypothesis and these constraints further hinder storage of information via padding of this hypothesis. It is shown that if q> 3, then simple external contextual languages are not iteratively learnable using a class preserving one-one hypothesis space, while for q = 1 it is iteratively learnable, even in polynomial time. It is also investigated for which choice of the parameters, the simple external contextual languages can be learnt by a consistent and conservative iterative learner. 1

Abstract. The present paper is a short reflection concerning the role which inductive inference played and can play in language learning. We shortly recall some major insights obtained and outline some new directions based on own work and results recently presented in the literature. 1