In formal language theory, computer science and linguistics, the Chomsky hierarchy is a containment hierarchy of classes of formal grammars.
A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by CSG but not by context-free grammars. Context-sensitive grammars are less general than unrestricted grammars. Thus, CSG are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
In theoretical computer science and formal language theory, a regular grammar is a grammar that is right-regular or left-regular. While their exact definition varies from textbook to textbook, they all require that
An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also been used to model the morphology of a variety of organisms and can be used to generate self-similar fractals.
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name.
In computer science, an LL parser is a top-down parser for a restricted context-free language. It parses the input from Left to right, performing Leftmost derivation of the sentence.
In computer science, extended Backus–Naur form (EBNF) is a family of metasyntax notations, any of which can be used to express a context-free grammar. EBNF is used to make a formal description of a formal language such as a computer programming language. They are extensions of the basic Backus–Naur form (BNF) metasyntax notation.
Grammar theory to model symbol strings originated from work in computational linguistics aiming to understand the structure of natural languages. Probabilistic context free grammars (PCFGs) have been applied in probabilistic modeling of RNA structures almost 40 years after they were introduced in computational linguistics.
Top-down parsing in computer science is a parsing strategy where one first looks at the highest level of the parse tree and works down the parse tree by using the rewriting rules of a formal grammar. LL parsers are a type of parser that uses a top-down parsing strategy.
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system".
Categorial grammar is a family of formalisms in natural language syntax which share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz, Yehoshua Bar-Hillel, and Joachim Lambek. It saw a surge of interest in the 1970s following the work of Richard Montague, whose Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics.
In computer science, a parsing expression grammar (PEG), is a type of analytic formal grammar, i.e. it describes a formal language in terms of a set of rules for recognizing strings in the language. The formalism was introduced by Bryan Ford in 2004 and is closely related to the family of top-down parsing languages introduced in the early 1970s. Syntactically, PEGs also look similar to context-free grammars (CFGs), but they have a different interpretation: the choice operator selects the first match in PEG, while it is ambiguous in CFG. This is closer to how string recognition tends to be done in practice, e.g. by a recursive descent parser.
In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language and a suffix. For instance, can be recognized as a sum because it can be broken into , also a sum, and , a suitable suffix.
Grammar induction is the process in machine learning of learning a formal grammar from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs.
In computer science, terminal and nonterminal symbols are the lexical elements used in specifying the production rules constituting a formal grammar. Terminal symbols are the elementary symbols of the language defined by a formal grammar. Nonterminal symbols are replaced by groups of terminal symbols according to the production rules.
Indexed grammars are a generalization of context-free grammars in that nonterminals are equipped with lists of flags, or index symbols. The language produced by an indexed grammar is called an indexed language.
In formal language theory, a grammar describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
Controlled grammars are a class of grammars that extend, usually, the context-free grammars with additional controls on the derivations of a sentence in the language. A number of different kinds of controlled grammars exist, the four main divisions being Indexed grammars, grammars with prescribed derivation sequences, grammars with contextual conditions on rule application, and grammars with parallelism in rule application. Because indexed grammars are so well established in the field, this article will address only the latter three kinds of controlled grammars.
