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Rule system for formal languages
theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular
Context-free_grammar
Formal grammar derived from a deterministic pushdown automaton
grammar theory, the deterministic context-free grammars (DCFGs) are a proper subset of the context-free grammars. They are the subset of context-free
Deterministic context-free grammar
Deterministic_context-free_grammar
Grammar model in linguistics
probabilistic context free grammars (PCFGs) extend context-free grammars, similar to how hidden Markov models extend regular grammars. Each production
Probabilistic context-free grammar
Probabilistic_context-free_grammar
Abstract language theory concept
Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition
Generalized context-free grammar
Generalized_context-free_grammar
Formal language generated by context-free grammar
theory, a context-free language (CFL), also called a Chomsky type-2 language, is a language generated by a context-free grammar (CFG). Context-free languages
Context-free_language
Type of formal grammar
surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that
Context-sensitive_grammar
Type of context-free grammar
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or
Ambiguous_grammar
Type of a context-free grammar
In formal language theory, an LL grammar is a context-free grammar that can be parsed by an LL parser, which parses the input from Left to right, and
LL_grammar
Topics referred to by the same term
Context-free may refer to: Context-free grammar Deterministic context-free grammar Generalized context-free grammar Probabilistic context-free grammar
Context-free
Type of grammar for describing formal 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
Parsing_expression_grammar
Synchronous context-free grammars (SynCFG or SCFG; not to be confused with stochastic CFGs) are a type of formal grammar designed for use in transfer-based
Synchronous context-free grammar
Synchronous_context-free_grammar
Hierarchy of classes of formal grammars
paper "The algebraic theory of context free languages" describes the modern hierarchy, including context-free grammars. Independently, alongside linguists
Chomsky_hierarchy
Family of formalisms in natural language syntax
any context-free language can be generated by a basic categorial grammar, recall that any context-free language can be generated by a context-free grammar
Categorial_grammar
Analysing a string of symbols, according to the rules of a formal grammar
not context-free, some kind of context-free approximation to the grammar is used to perform a first pass. Algorithms which use context-free grammars often
Parsing
Structure of a formal language
language can alternatively be generated by a context-free, nonambiguous grammar; for instance, the regular grammar with rules 1. S → a S {\displaystyle S\rightarrow
Formal_grammar
Parsing algorithm for context-free grammars
algorithm (alternatively called CYK, or CKY) is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. The algorithm is named after
CYK_algorithm
Non-language factors that enhance understanding of communication
context-sensitive grammar, where the applicability of a production rule may depend on the surrounding context of symbols. Unlike context-free grammars, which can
Context
Notation for context-free formal grammars
In formal language theory, a context-free grammar, G, is said to be in Chomsky normal form (first described by Noam Chomsky) if all of its production rules
Chomsky_normal_form
Machine-learning process
inference of context-free grammars and richer formalisms, such as multiple context-free grammars and parallel multiple context-free grammars. Other classes
Grammar_induction
Form for context-free grammars
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
Greibach_normal_form
(This is typically handled by a Chomsky Type 2 grammar, also termed a context-free grammar.) Context-free languages are a category of languages (sometimes
Comparison of parser generators
Comparison_of_parser_generators
Computer science and linguistics concept relating to non-terminal production
context-free grammar produces a finite or infinite language. Nederhof, Mark-Jan; Satta, Giorgio (2002), "Parsing Non-recursive Context-free Grammars"
Recursive_grammar
Language consisting of balanced strings of brackets
the Dyck language via a context-free grammar in some situations. The Dyck language is generated by the context-free grammar with a single non-terminal
Dyck_language
Formal language models
Joshi characterized "grammars (and associated languages) that are only slightly more powerful than context-free grammars (context-free languages)". He called
Mildly context-sensitive grammar formalism
Mildly_context-sensitive_grammar_formalism
Type of grammar based on constituent entities
restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars. In a broader sense, phrase structure grammars are also
Phrase_structure_grammar
Language defined by context-sensitive grammar
the surrounding context of symbols. Unlike context-free grammars, which can apply rules regardless of context, context-sensitive grammars allow rules to
Context-sensitive_language
Grammar formalism
Tree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi. Tree-adjoining grammars are somewhat similar to context-free grammars, but the
Tree-adjoining_grammar
Visual description of context-free grammar
a context-free grammar. They represent a graphical alternative to Backus–Naur form, EBNF, Augmented Backus–Naur form, and other text-based grammars as
Syntax_diagram
operator precedence grammar is a kind of grammar for formal languages. Technically, an operator precedence grammar is a context-free grammar that has the property
Operator-precedence_grammar
Notation techniques for grammars in computer science
defined by a pair of grammars, that operate on different levels: the hypergrammar is an attribute grammar, i.e. a set of context-free grammar rules in which
Van_Wijngaarden_grammar
When formal languages generate the same set of strings
respectively for context-free grammars: see Context-free grammar#Context-free language for a formal definition for context-free grammars: concrete syntax
Equivalence (formal languages)
Equivalence_(formal_languages)
Term in linguistic syntax
be shown by Ogden's lemma. Suppose the language is generated by a context-free grammar, then let p {\displaystyle p} be the length required in Ogden's lemma
Cross-serial_dependencies
context-free: Context-free grammar#Subclasses; context-free languages are closed with respect to union and (even general) concatenation: Context-free
Greibach's_theorem
Subset of languages in formal theory
even-length palindromes on the alphabet of 0 and 1 has the unambiguous context-free grammar S → 0S0 | 1S1 | ε. An arbitrary string of this language cannot be
Deterministic context-free language
Deterministic_context-free_language
Lossless data compression algorithm
Grammar-based codes or grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar (CFG) for the string
Grammar-based_code
Parameter estimation method for probabilistic context-free grammars
way of re-estimating production probabilities in a probabilistic context-free grammar. It was introduced by James K. Baker in 1979 as a generalization
Inside–outside_algorithm
In computer science, a linear grammar is a context-free grammar that has at most one nonterminal in the right-hand side of each of its productions. A
Linear_grammar
Top-down parser utilizing recursion
The LL(k) grammars therefore exclude all ambiguous grammars, as well as all grammars that contain left recursion. Any context-free grammar can be transformed
Recursive_descent_parser
Type of formal grammar
Straight-line grammars (more precisely: straight-line context-free string grammars) can be generalized to Straight-line context-free tree grammars. The latter
Straight-line_grammar
theory of formal languages, the smallest grammar problem is the problem of finding the smallest context-free grammar that generates a given string of characters
Smallest_grammar_problem
Controlled grammars are a class of grammars that extend, usually, the context-free grammars with additional controls on the derivations of a sentence in
Controlled_grammar
Type of automaton
equivalent to conjunctive grammars in the same way as nondeterministic PDA are equivalent to context-free grammars. Context-free grammar Counter automaton Finite-state
Pushdown_automaton
Formal means of expressing grammar
only express context-free grammars; there is only one argument on the left side of the production. However, context-sensitive grammars can also be expressed
Definite_clause_grammar
class of grammars which are parsable in this way is known as the LL grammars. LL grammars are an even more restricted class of context-free grammars than
History of compiler construction
History_of_compiler_construction
Problem in computer programming
nested conditional statements ambiguous. Formally, the reference context-free grammar of the language is ambiguous, meaning there is more than one correct
Dangling_else
Theorem concerning occurrences of terminal symbols in context-free languages
that strings with a given number of terminals are not accepted by a context-free grammar. It was first proved by Rohit Parikh in 1961 and republished in 1966
Parikh's_theorem
World Wide Web Consortium standard
form have the expressive power of a context-free grammar. A grammar processor that does not support recursive grammars has the expressive power of a finite-state
Speech Recognition Grammar Specification
Speech_Recognition_Grammar_Specification
Formal grammar
cumbersome or impossible constructions in traditional context-free grammars. Adaptive grammars find applications in natural language processing, extensible
Adaptive_grammar
Algorithmic problem with applications to program analysis
analysis. Given a graph with edge labels from some alphabet and a context-free grammar over that alphabet, the problem is to determine whether there exists
Context-free language reachability
Context-free_language_reachability
Sequence of words formed by specific rules
language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. In computer science, formal languages are used
Formal_language
György Révész transforms a grammar in Kuroda normal form to a context-sensitive grammar: AB → CD is replaced by four context-sensitive rules AB → AZ, AZ
Kuroda_normal_form
Higher-order function that combines several parsers
ambiguous context-free grammar, s ::= ‘x’ s s | ε. Using the combinators defined earlier, we can modularly define executable notations of this grammar in a
Parser_combinator
Tree in formal language theory
represents the syntactic structure of a string according to some context-free grammar. The term parse tree itself is used primarily in computational linguistics;
Parse_tree
Meter and form of classical Tamil poetry
classified based upon the rules of metric prosody. Such rules form a context-free grammar. Every venba consists of between two and twelve lines. The venpa
Venpa
American computer scientist (1946–2023)
included work in the subareas of part-of-speech tagging, probabilistic context-free grammar induction, and, more recently, syntactic disambiguation through word
Eugene_Charniak
Family of metasyntax notations
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
Extended_Backus–Naur_form
Algorithm for parsing context-free languages
( n 2 ) {\displaystyle O(n^{2})} quadratic space for all other context-free grammars, where n {\displaystyle n} is the length of the parsed string. The
Earley_parser
Recursive algorithm for data compression
and Ian H. Witten in 1997 that infers a hierarchical structure (context-free grammar) from a sequence of discrete symbols. The algorithm operates in linear
Sequitur_algorithm
Grammar model in linguistics
stochastic grammar (statistical grammar) is a grammar framework with a probabilistic notion of grammaticality: Stochastic context-free grammar Statistical
Stochastic_grammar
the number of words of a given length generated by an unambiguous context-free grammar. The theorem provides an unexpected link between the theory of formal
Chomsky–Schützenberger enumeration theorem
Chomsky–Schützenberger_enumeration_theorem
Type of formal grammar
Edgar T. "Ned" Irons, the author of IMP. The following is a simple context-free grammar which can describe a language made up of multiplication and addition
Attribute_grammar
Rewriting system and type of formal grammar
L-system's grammar. An L-system is context-free if each production rule refers only to an individual symbol and not to its neighbours. Context-free L-systems
L-system
Type of parser in computer science
LR ( k ) {\displaystyle \operatorname {LR} (k)} is now short: A context-free grammar G {\displaystyle G} is called LR ( k ) {\displaystyle \operatorname
LR_parser
is a graph theoretical schematic used to represent the rules of a context-free grammar. RTNs have application to programming languages, natural language
Recursive_transition_network
Form of source code, without regard to meaning
Backus–Naur form (BNF). Phrase grammars are often specified in much more constrained grammars than full context-free grammars, in order to make them easier
Syntax (programming languages)
Syntax_(programming_languages)
Type of formal grammar
Ullman 1979, p. 217 (left, right-regular grammars as subclasses of context-free grammars), p. 79 (context-free grammars). Hopcroft & Ullman 1979, p. 229, exercise
Regular_grammar
parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton, but instead of using
Embedded_pushdown_automaton
Stuart M. Shieber. It uses context-free grammar rules and feature constraints on these rules. Head-driven phrase structure grammar PC-PATR, an implementation
PATR-II
to define context-free grammars: that is, a formal way to describe formal languages. It can express the entire range of context-free grammars. Its current
Syntax_Definition_Formalism
Earliest model of generative grammar
important feature of all transformational grammars is that they are more powerful than context-free grammars. Chomsky formalized this idea in the Chomsky
Transformational_grammar
Symbolic representation of information using visualization techniques
techniques exist. Some more examples follow: Look up diagram in Wiktionary, the free dictionary. commons:Specific diagram types – Gallery of many diagram types
Diagram
Generalization of the pumping lemma for context-free languages
Ogden's lemma—If a language L {\displaystyle L} is generated by a context-free grammar, then there exists some p ≥ 1 {\displaystyle p\geq 1} such that for
Ogden's_lemma
Top-down parser that parses input from left to right
Lewis (1969). For a given context-free grammar, the parser attempts to find the leftmost derivation. Given an example grammar G: S → E {\displaystyle S\to
LL_parser
Processing of natural language by a computer
probabilistic context-free grammar (PCFG) (see also stochastic grammar). Lexical semantics What is the computational meaning of individual words in context? Distributional
Natural_language_processing
Grammar formalism
non-context-free affix grammar. The string quartet was published in 1968, as Mathematical Centre Report MR 96. The grammatical rules of an affix grammar are
Affix_grammar
Language theory
Indexed grammars are a generalization of context-free grammars in that nonterminals are equipped with lists of flags, or index symbols. The language produced
Indexed_grammar
Theory of computer sciences
sum, and + 3 {\displaystyle {}+3} , a suitable suffix. In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of
Left_recursion
Lossless, but memory-consuming, data compression algorithm
pairing) is a grammar-based compression algorithm that, given an input text, builds a straight-line program, i.e. a context-free grammar generating a single
Re-Pair
algorithm for parsing context-free grammars in Chomsky normal form Earley parser: another O(n3) algorithm for parsing any context-free grammar GLR parser: an
List_of_algorithms
Categories of symbols in formal grammars
non-trivial; not all languages can be generated by context-free grammars. Those that can are called context-free languages. These are exactly the languages that
Terminal and nonterminal symbols
Terminal_and_nonterminal_symbols
Parser generator
parser (LALR parser) in the programming language C from an input context-free grammar. The generator is quite simple, implemented in one C source file
Lemon_(parser_generator)
Rice gave an alternative definition of context-free grammars by language equations. To every context-free grammar G = ( V , Σ , R , S ) {\displaystyle G=(V
Language_equation
structures to be transformed, specified as a (possibly ambiguous) context-free grammar using an extended Backus–Naur Form; and a set of tree transformation
TXL_(programming_language)
Context-free formal grammar
In computer science, a simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser. The concept was first
Simple_precedence_grammar
Breadth of ideas which can be represented in a formal language
describe sets of strings, such as context-free grammars and regular expressions. Each instance of a formalism, e.g. each grammar and each regular expression
Expressive power (computer science)
Expressive_power_(computer_science)
Topics referred to by the same term
developing software applications Syntax-Directed Definition - a context-free grammar with attributes and rules Sentential Decision Diagram, a formalism
SDD
Formalism to describe programming languages
developed by John Backus and Peter Naur. It is a metasyntax for context-free grammars, providing a precise way to outline the rules of a language's structure
Backus–Naur_form
tool that reads a context-free grammar (CFG) and creates an LALR parser which is capable of parsing files written in the context-free language defined
LALR_parser_generator
Type of chart parser
a left corner parser is a type of chart parser used for parsing context-free grammars. It combines the top-down and bottom-up approaches of parsing. The
Left_corner_parser
Method of symbol substitution
of formal grammar in the Chomsky hierarchy impose additional restrictions on what constitutes a production. Notably in a context-free grammar, the left-hand
Production_(computer_science)
Type of pumping lemma
pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all context-free languages and generalizes
Pumping lemma for context-free languages
Pumping_lemma_for_context-free_languages
Type of machine learning model
communication technologist Vyvyan Evans mapped out the role of probabilistic context-free grammar (PCFG) in enabling NLP to model cognitive patterns and generate human-like
Large_language_model
Topics referred to by the same term
Glycomics, a biochemical research initiative Context-free grammar, in computer science, a type of formal grammar Control-flow graph, in computer science,
CFG
Software that translates code from one programming language to another
Backus and used for the syntax of Algol 60. The ideas derive from the context-free grammar concepts by linguist Noam Chomsky. "BNF and its extensions have become
Compiler
Educational software
pushdown automata context-free grammar proof on wikt:nondeterministic pushdown automaton to context-free grammar proof on context-free grammar to pushdown automaton
JFLAP
Tree representation of the abstract syntactic structure of source code
avoid this ambiguity, programming languages are often specified as a context-free grammar (CFG). However, there are often aspects of programming languages
Abstract_syntax_tree
Ability to solve a problem by an effective procedure
accepted by a pushdown automaton as a Context-free language, which can be specified as a Context-free grammar. The language consisting of strings with
Computability
Compiler-generation system
non-deterministic) for all kinds of context-free grammars (CFGs) as well as some classes of contextual grammars.[citation needed] It has been developed
SYNTAX
Overview of and topical guide to machine learning
recognition Prisma (app) Probabilistic Action Cores Probabilistic context-free grammar Probabilistic latent semantic analysis Probabilistic soft logic Probability
Outline_of_machine_learning
of grammars, the context-free grammars, with conjunction and negation operations. Besides these explicit operations, Boolean grammars allow implicit disjunction
Boolean_grammar
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