A deterministic pushdown automaton (dpda) having just one stack symbol is called a deterministic restricted one-counter automaton (droca). When it accepts an input by empty stack, it is called strict. This paper is concerned with a subclass of real-time strict droca's, called Szilard strict droca's, and studies the problem of identifying the subclass in the limit from positive data. The class of languages accepted by Szilard strict droca's coincides with the class of Szilard languages (or, associated languages) of strict droca's and is incomparable to each of the class of regular languages and that of simple languages. After providing some properties of languages accepted by Szilard strict droca's, we show that the class of Szilard strict droca's is polynomial time identifiable in the limit from positive data in the sense of Yokomori. This identifiability is proved by giving an exact characteristic sample of polynomial size for a language accepted by a Szilard strict droca. The class of very simple languages, which is a proper subclass of simple languages, is also proved to be polynomial time identifiable in the limit from positive data by Yokomori, but it is yet unknown whether there exists a characteristic sample of polynomial size for any very simple language.

This paper considers properties of language classes with finite elasticity in the viewpoint of set theoretic operations. Finite elasticity was introduced by Wright as a sufficient condition for language classes to be inferable from positive data, and as a property preserved by (not usual) union operation to generate a class of unions of languages. We show that the family of language classes with finite elasticity is closed under not only union but also various operations for language classes such as intersection, concatenation and so on, except complement operation. As a framework defining languages, we introduce restricted elementary formal systems (EFS's for short), called max length-bounded by which any context-sensitive language is definable. We define various operations for EFS's corresponding to usual language operations and also for EFS classes, and investigate closure properties of the family Ge of max length-bounded EFS classes that define classes of languages with finite elasticity. Furthermore, we present theorems characterizing a max length-bounded EFS class in the family Ge, and that for the language class to be inferable from positive data, provided the class is closed under subset operation. From the former, it follows that for any n, a language class definable by max length-bounded EFS's with at most n axioms has finite elasticity. This means that Ge is sufficiently large.

In this paper, we deal with inductive inference of an indexed family of recursive languages. We give two sufficient conditions for inductive inferability of an indexed family from positive data, each of which does not depend on the indexing of the family. We introduce two notions of finite cross property for a class of languages and a pair of finite tell-tales for a language. The former is a generalization of finite elasticity due to Wright and the latter consists of two finite sets of strings one of which is a finite tell-tale introduced by Angluin. The main theorem in this paper is that if any language of a class has a pair of finite tell-tales, then the class is inferable from positive data. Also, it is shown that any language of a class with finite cross property has a pair of finite tell-tales. Hence a class with finite cross property is inferable from positive data. Further-more, it is proved that a language has a finite tell-tale if and only if there does not exist any infinite cross sequence of languages contained in the language.

In this paper, we consider the polynomial time inferability from positive data for unions of two tree pattern languages. A tree pattern is a structured pattern known as a term in logic programming, and a tree pattern language is the set of all ground instances of a tree pattern. We present a polynomial time algorithm to find a minimal union of two tree pattern languages containing given examples. Our algorithm can be considered as a natural extension of Plotkin's least generalization algorithm, which finds a minimal single tree pattern language. By using this algorithm, we can realize a consistent and conservative polynomial time inference machine that identifies unions of two tree pattern languages from positive data in the limit.