On Context-Sensitive Grammars

Abstract

This is an overview on context-sensitive grammars. The paper contains also an appendix about Chomsky type-0 grammars (also called phrase-structure grammars). These grammars and families of languages are arising in classical language theory. Most of the topics presented in this paper are in some sense modifications of the classical notion of a rewriting system, introduced by Axel Thue at the beginning of 20th century, [44]. A rewriting system is a (finite) set of rules u → ν, where u and ν are words, indicating that an occurrence of u (as a subword) can be replaced by ν. A rewriting system only transforms words into other words, languages into other languages. After supplementing it with some mechanism for “squeezing out” a language, a rewriting system can be used as a device for defining languages. This is what Chomsky did, with linguistic goals in mind, when he introduced different types of grammars, [3, 4, 5], see also [6]. At the beginning, the classification was not very clear but by mid-60’s the four classes of the Chomsky hierarchy of grammars and languages have become pretty standard: recursively enumerable,or of type 0; context-sensitive, or of type 1; context-free, or of type 2; regular,or of type 3.KeywordsTuring MachineRegular LanguageSentential FormTerminal SymbolInput TapeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.