Topic
Chomsky hierarchy
About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.
Papers published on a yearly basis
Papers
More filters
08 Oct 2019
TL;DR: This work provides a fixpoint characterization of the languages recognized by an indexed grammar and studies possible ways to abstract, in the abstract interpretation sense, these languages and their grammars into context-free and regular languages.
Abstract: Indexed grammars are a generalization of context-free grammars and recognize a proper subset of context-sensitive languages. The class of languages recognized by indexed grammars are called indexed languages and they correspond to the languages recognized by nested stack automata. For example indexed grammars can recognize the language Open image in new window which is not context-free, but they cannot recognize Open image in new window which is context-sensitive. Indexed grammars identify a set of languages that are more expressive than context-free languages, while having decidability results that lie in between the ones of context-free and context-sensitive languages. In this work we study indexed grammars in order to formalize the relation between indexed languages and the other classes of languages in the Chomsky hierarchy. To this end, we provide a fixpoint characterization of the languages recognized by an indexed grammar and we study possible ways to abstract, in the abstract interpretation sense, these languages and their grammars into context-free and regular languages.
3 citations
3 citations
Journal Article•
3 citations
28 Apr 2005
TL;DR: The relevance of the notion of k-valued categorial grammars where a word is associated to at most k types is established for two related grammatical systems as a fruitful constraint for obtaining several properties like the existence of learning algorithms.
Abstract: The notion of k-valued categorial grammars where a word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of k-valued grammars correspond to a real hierarchy of languages. This paper establishes the relevance of this notion for two related grammatical systems. In the first part, the classes of k-valued non-associative Lambek (NL) grammars without product is proved to define a strict hierarchy of languages. The second part introduces the notion of generalized functor argument for non-associative Lambek (NL∅) calculus without product but allowing empty antecedent and establishes also that the classes of k-valued (NL∅) grammars without product form a strict hierarchy of languages.
3 citations