Topic
Indexed language
About: Indexed language is a research topic. Over the lifetime, 334 publications have been published within this topic receiving 11000 citations.
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07 Jul 2003
TL;DR: The lower and upper bounds for sizes of test sets for the families of all languages, of commutative languages, for regular languages and of context-free languages are studied.
Abstract: We study the lower and upper bounds for sizes of test sets for the families of all languages, of commutative languages, of regular languages and of context-free languages.
TL;DR: The decidability of the equivalence of grammars with respect to the differentiation function and structure function is discussed and the decidable of the k -narrowness of context-free Grammars is proved.
Abstract: We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. A grammar is called narrow (or k -narrow) iff its differentiation function is bounded by a constant (by k ). We present the basic properties of differentiation functions, especially we relate them to structure function of context-free languages and narrow grammars to slender languages. We discuss the decidability of the equivalence of grammars with respect to the differentiation function and structure function and prove the decidability of the k -narrowness of context-free grammars. Furthermore, we introduce languages representing the graph of the differentiation and structure function and relate these languages to those of the Chomsky hierarchy.
Journal Article•
TL;DR: The goal is to explore the situation when a more coarse classification of input languages is possible, whereas more refined classification is not, and to answer the following question: under which conditions, a learner, being fed n different languages, can produce m grammars covering all input languages, but cannot produce k grammARS covering input languages for any k > m.
Abstract: We consider a variant of Gold's learning paradigm where a learner receives as input n different languages (in form of one text where all input languages are interleaved). Our goal is to explore the situation when a more coarse classification of input languages is possible, whereas more refined classification is not. More specifically, we answer the following question: under which conditions, a learner, being fed n different languages, can produce m grammars covering all input languages, but cannot produce k grammars covering input languages for any k > m. We also consider a variant of this task, where each of the output grammars may not cover more than r input languages. Our main results indicate that the major factor affecting classification capabilities is the difference n - m between the number n of input languages and the number m of output grammars. We also explore relationship between classification capabilities for smaller and larger groups of input languages. For the variant of our model with the upper bound on the number of languages allowed to be represented by one output grammar, for classes consisting of disjoint languages, we found complete picture of relationship between classification capabilities for different parameters n (the number of input languages), m (number of output grammars), and r (bound on the number of languages represented by each output grammar). This picture includes a combinatorial characterization of classification capabilities for the parameters n, m, r of certain types.
TL;DR: The Ai are auxiliary symbois and can bepreted as a homomorphism from Ri to W.