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Formal language generated by context-free grammar
In formal language 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_language
Rule system for formal languages
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of
Context-free_grammar
Subset of languages in formal theory
formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are context-free languages that
Deterministic context-free language
Deterministic_context-free_language
Type of pumping lemma
In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma
Pumping lemma for context-free languages
Pumping_lemma_for_context-free_languages
Type of context-free grammar
a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language
Ambiguous_grammar
Language defined by context-sensitive grammar
In formal language theory, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar, where the applicability
Context-sensitive_language
Topics referred to by the same term
Synchronous context-free grammar Context-free language Deterministic context-free language All pages with titles containing Context-free Context (disambiguation)
Context-free
Algorithmic problem with applications to program analysis
Context-free language reachability is an algorithmic problem with applications in static program analysis. Given a graph with edge labels from some alphabet
Context-free language reachability
Context-free_language_reachability
Hierarchy of classes of formal grammars
theory of formal languages; the paper "The algebraic theory of context free languages" describes the modern hierarchy, including context-free grammars. Independently
Chomsky_hierarchy
Formal grammar derived from a deterministic pushdown automaton
deterministic pushdown automata, and they generate the deterministic context-free languages. DCFGs are always unambiguous, and are an important subclass of
Deterministic context-free grammar
Deterministic_context-free_grammar
Type of formal grammar
positioned between context-free and unrestricted grammars in the Chomsky hierarchy. A formal language that can be described by a context-sensitive grammar
Context-sensitive_grammar
Term in linguistic syntax
the syntactic structure of natural language; languages containing an arbitrary number of them are non-context-free. By this fact, Dutch and Swiss-German
Cross-serial_dependencies
Non-language factors that enhance understanding of communication
fundamental principle in language was contextuality or compositionality, and compositionality was usually preferred. Verbal context refers to the text or
Context
Formal language models
(context-free languages)". He called these grammars mildly context-sensitive grammars and the associated languages mildly context-sensitive languages.
Mildly context-sensitive grammar formalism
Mildly_context-sensitive_grammar_formalism
Generalization of the pumping lemma for context-free languages
theory of formal languages, Ogden's lemma (named after William F. Ogden) is a generalization of the pumping lemma for context-free languages. Despite Ogden's
Ogden's_lemma
Structure of a formal language
or b {\displaystyle b} as we please. That same language can alternatively be generated by a context-free, nonambiguous grammar; for instance, the regular
Formal_grammar
Algorithm for parsing context-free languages
parser is an algorithm for parsing strings that belong to a given context-free language. Named after its inventor Jay Earley, it was first introduced in
Earley_parser
Sequence of words formed by specific rules
language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free
Formal_language
Computer science and linguistics concept relating to non-terminal production
whether a context-free grammar produces a finite or infinite language. Nederhof, Mark-Jan; Satta, Giorgio (2002), "Parsing Non-recursive Context-free Grammars"
Recursive_grammar
Form of source code, without regard to meaning
divided into context-free syntax and context-sensitive syntax. Context-free syntax are rules directed by the metalanguage of the programming language. These
Syntax (programming languages)
Syntax_(programming_languages)
Grammar model in linguistics
linguistics and computational linguistics, probabilistic context free grammars (PCFGs) extend context-free grammars, similar to how hidden Markov models extend
Probabilistic context-free grammar
Probabilistic_context-free_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 constructs
LL_grammar
Chomsky Type 2 grammar, also termed a context-free grammar.) Context-free languages are a category of languages (sometimes termed Chomsky Type 2) which
Comparison of parser generators
Comparison_of_parser_generators
Type of automaton
recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in
Pushdown_automaton
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
Lemma that defines a property of regular languages
simplification of their pumping lemma for context-free languages. Let L {\displaystyle L} be a regular language. Then there exists an integer p ≥ 1 {\displaystyle
Pumping lemma for regular languages
Pumping_lemma_for_regular_languages
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
Type of grammar for describing formal languages
exist context-free languages that cannot be recognized by a PEG, but this is not yet proven. PEGs are well suited to parsing computer languages (and artificial
Parsing_expression_grammar
Chemical species structure notation
encountered. From the view point of a formal language theory, SMILES is a word. A SMILES is parsable with a context-free parser. The use of this representation
Simplified Molecular Input Line Entry System
Simplified_Molecular_Input_Line_Entry_System
Theorem concerning occurrences of terminal symbols in context-free languages
terminal symbol in a context-free language, without regard to their order, then the language is indistinguishable from a regular language. It is useful for
Parikh's_theorem
Top-down parser that parses input from left to right
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
LL_parser
formal languages, the interchange lemma states a necessary condition for a language to be context-free, just like the pumping lemma for context-free languages
Interchange_lemma
Type of parser in computer science
parsers are a type of bottom-up parser that analyse deterministic context-free languages in linear time. There are several variants of LR parsers: SLR parsers
LR_parser
Formal languages in computing
indexed languages has practical importance in natural language processing as a computationally affordable[citation needed] generalization of context-free languages
Indexed_language
Notation techniques for grammars in computer science
of programming languages, most notably, of ALGOL 60, which introduced a syntax description in Backus–Naur form. However, context-free rules cannot express
Van_Wijngaarden_grammar
Language consisting of balanced strings of brackets
helpful to define the Dyck language via a context-free grammar in some situations. The Dyck language is generated by the context-free grammar with a single
Dyck_language
Formal language
Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive
Recursively enumerable language
Recursively_enumerable_language
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 by the
LALR_parser_generator
Sequence that reads the same forwards and backwards
automata theory, the set of all palindromes over an alphabet is a context-free language, but it is not regular. The word palindrome was introduced by English
Palindrome
Abstract machine in computer science
pushdown automata accepts the deterministic context-free languages, a proper subset of context-free languages. Machine transitions are based on the current
Deterministic pushdown automaton
Deterministic_pushdown_automaton
regular languages, the context-free languages and the recursively enumerable languages, and other families of formal languages studied in the scientific
Abstract_family_of_languages
grammar is a context-free grammar that has at most one nonterminal in the right-hand side of each of its productions. A linear language is a language generated
Linear_grammar
Topics referred to by the same term
Look up context (disambiguation) in Wiktionary, the free dictionary. Context is the relevant constraints of the communicative situation that influence
Context_(disambiguation)
Type of machine learning model
processing tasks, especially language generation. LLMs can typically generate, summarize, translate, and analyze text in many contexts, and are a foundational
Large_language_model
Function defined on formal languages in computer science
which are equivalent to context-free grammars. This insight was used to derive parsing algorithms for context-free languages. Implementation of such algorithms
Brzozowski_derivative
Given a context-free language, is it inherently ambiguous? Proof: The class of context-free languages, and the set of context-free languages that aren't
Greibach's_theorem
Study of abstract machines and automata
closely related to formal language theory. In this context, automata are used as finite representations of formal languages that may be infinite. Automata
Automata_theory
Ability to solve a problem by an effective procedure
for context-free languages. An example of such a language is the set of prime numbers. Turing machines can decide any context-free language(language accepted
Computability
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
When formal languages generate the same set of strings
<factor>, 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)
Algorithm that combines tokenization and parsing
level makes the language recognized by the parser a single context-free language defined on characters, as opposed to a context-free language of sequences
Scannerless_parsing
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
Artificial intelligence chatbot by Moonshot AI
version, released in 2023, was known for supporting up to 128,000 tokens of context. The company released the open-weights Kimi K2 in July 2025, and Kimi K3
Kimi_(AI)
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
Chomsky_normal_form
Theorem in algebra
states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by David Muller and Paul
Muller–Schupp_theorem
particular by the families of regular languages, context-free languages and the recursively enumerable languages. The concept of a cone is a more abstract
Cone_(formal_languages)
Social context in understanding culture
relations, body language, verbal messages, or non-verbal messages. "High-" and "low-" context cultures typically refer to language groups, nationalities
High-context and low-context cultures
High-context_and_low-context_cultures
American computer scientist
languages accepted with finite delay. Hence the family of deterministic context-free language is a principal AFDL; there is a context-free language L
Sheila_Greibach
Topics referred to by the same term
Look up context-sensitive in Wiktionary, the free dictionary. Context-sensitive is an adjective meaning "depending on context" or "depending on circumstances"
Context-sensitive
Esoteric, minimalist programming language
brackets must be properly matched, making the set of valid programs a context-free language. Many practical implementations allocate a finite array of cells
Brainfuck
Overview of and topical guide to natural language processing
with 'Sally', the sentence's subject. Context-free language – Controlled natural language – a natural language with a restriction introduced on its grammar
Outline of natural language processing
Outline_of_natural_language_processing
Representing a given context-free language in terms of two simpler languages
a given context-free language in terms of two simpler languages. These two simpler languages, namely a regular language and a Dyck language, are combined
Chomsky–Schützenberger representation theorem
Chomsky–Schützenberger_representation_theorem
Index of articles associated with the same name
that certain languages are not regular Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair
Pumping_lemma
Formal language concept
language class lies properly between the regular languages and the deterministic context-free languages. Since their introduction in 2004, these concepts
Nested_word
generated by an unambiguous context-free grammar. The theorem provides an unexpected link between the theory of formal languages and abstract algebra. In
Chomsky–Schützenberger enumeration theorem
Chomsky–Schützenberger_enumeration_theorem
Formal language in mathematics and computer science
of language was not defined in the Chomsky hierarchy. All recursive languages are also recursively enumerable. All regular, context-free and context-sensitive
Recursive_language
Family of formalisms in natural language syntax
capacity to context-free grammars and are thus often considered inadequate for theories of natural language syntax. Unlike context-free grammars, categorial
Categorial_grammar
Complexity class
of context-free languages recognized by deterministic pushdown automata, is contained in SC, as shown by Cook in 1979. It is open if all context-free languages
SC_(complexity)
Educational software
pushdown automaton to context-free grammar proof on context-free grammar to pushdown automaton pumping lemma for context-free language CYK parser LL parser
JFLAP
Complexity class of decision problems
single algorithm that satisfies both constraints. Deterministic context-free languages can be recognized in SC. SC contains Randomized L and Bounded-Error
PolyL
Canadian computer scientist (born 1941)
the nested-stack automaton as vehicles for extending the power of context-free languages, but retaining many of their decidability and closure properties
Alfred_Aho
Set of strings closed w.r.t. cyclic shift, repetition, and root
the language is cyclic, but not regular. However, L is context-free, since M = { an1bn1 an2bn2 ... ank bnk : ni ≥ 0 } is, and context-free languages are
Cyclic_language
computational model for parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton
Embedded_pushdown_automaton
West Germanic language
pp. 1–56. Romaine, Suzanne (2006). "Language Policy in Multilingual Educational Contexts". Encyclopedia of Language & Linguistics. pp. 584–596. doi:10
English_language
Family of large language models by Google
SigLIP vision encoder. Every model has a context length of 128K, with the exception of Gemma 3 1B, which has a context length of 32K. Quantized versions fine-tuned
Gemma_(language_model)
Allowable structure and composition of phrases and sentences of a metalanguage
formal metalanguages used for describing recursive languages (formally called context-free languages) that have terminals, nonterminals, and metasymbols
Metasyntax
used to represent the rules of a context-free grammar. RTNs have application to programming languages, natural language and lexical analysis. Any sentence
Recursive_transition_network
Earliest model of generative grammar
the structure of natural languages with context-free grammars. His general position on the context-dependency of natural language has held up, though his
Transformational_grammar
Grammar formalism
somewhat similar to context-free grammars, but the elementary unit of rewriting is the tree rather than the symbol. Whereas context-free grammars have rules
Tree-adjoining_grammar
regular language and a context-free language is also closed, and it has been known at least since Hartmanis that the intersection of two context-free languages
Syntactic_predicate
Language theory
a generalization of context-free grammars in that nonterminals are equipped with lists of flags, or index symbols. The language produced by an indexed
Indexed_grammar
Algorithm used to analyze and process programming languages
repetitive and hard to understand. LR(k) can handle all deterministic context-free languages. In the past this LR(k) parser has been avoided because of its huge
Canonical_LR_parser
Model of learning
can be noticed without prior experience, what the Skill Model calls "context-free features." Think of the read-outs on the speedometer, tachometer and
Dreyfus model of skill acquisition
Dreyfus_model_of_skill_acquisition
Topics referred to by the same term
derived by Noam Chomsky and Marcel-Paul Schützenberger concerning context-free languages: The Chomsky–Schützenberger enumeration theorem about the number
Chomsky–Schützenberger theorem
Chomsky–Schützenberger_theorem
Mathematical concept and applications in software development
being a cyclic language. The operation shift(L) has been studied in formal language theory. For instance, if L is a context-free language, then shift(L)
Circular_shift
pattern languages is incomparable with the class of finite languages, with the class of regular languages, and with the class of context-free languages: the
Pattern language (formal languages)
Pattern_language_(formal_languages)
Sequence of characters that forms a search pattern
expressive power as regular grammars. But the language of regular expressions itself, is context-free language. Regular expressions consist of constants,
Regular_expression
Type of formal grammar
grammars (more precisely: straight-line context-free string grammars) can be generalized to Straight-line context-free tree grammars. The latter can be used
Straight-line_grammar
Categories of symbols in formal grammars
not all languages can be generated by context-free grammars. Those that can are called context-free languages. These are exactly the languages that can
Terminal and nonterminal symbols
Terminal_and_nonterminal_symbols
Computational learning model
finite languages and pattern languages) incomparable to regular and to context-free language class: Theorem 3.10, p.53 Gold, E. Mark (1964). Language identification
Language identification in the limit
Language_identification_in_the_limit
stack automata recognises exactly the languages generated by multiple context-free grammars (or linear context-free rewriting systems). For a finite and
Tree_stack_automaton
Free licensed works in any field
Free content, libre content, or open content (also called free information, libre information, open information) is any kind of creative work, such as
Free_content
Parsing algorithm for context-free languages
parser based on a modification of LL parsers to recognize languages described by any context-free grammar. While the theory behind "generalising" deterministic
GLL_parser
Language-oriented programming paradigm
Controlled natural language Context-free language Domain-specific language (or DSL) End-user programming Knowledge representation Natural-language processing
Natural_language_programming
TREEMETA) Translator Writing System is a compiler-compiler system for context-free languages originally developed in the 1960s. Parsing statements of the metalanguage
TREE-META
Israeli mathematician
Shelah. The pumping lemma for context-free languages, a widely used method for proving that a language is not context-free that Perles discovered with Yehoshua
Micha_Perles
Computational complexity class
decision problems that can be reduced in logarithmic space to a context-free language. This class is closed under complementation. It is situated between
LOGCFL
condition. In GTDPL it is straightforward to express interesting non-context-free languages such as the classic example {anbncn}. A GTDPL grammar can be reduced
Top-down_parsing_language
General-purpose document processor, derived from TeX
and uses a document markup language for manuscript preparation. The typographical and automated capabilities of ConTeXt are extensive, including interfaces
ConTeXt
used 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
Syntax_Definition_Formalism
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
Surname or Lastname
English
English : from Old French and Middle English frere ‘friar’ (Latin frater, literally ‘brother’). This was a status name for a member a religious order, especially a mendicant order, and may also have been a nickname for a pious person or for someone employed at a monastery.Americanized spelling of French Frère (see Frere).North German and Dutch : cognate of Friedrich.
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Telugu
Content
Boy/Male
Australian, British, English
In Liberty
Surname or Lastname
English (mainly southeastern)
English (mainly southeastern) : topographic name for someone who lived near a conspicuous tree, Middle English tre(w).
Girl/Female
Hindu
Content
Female
English
Anglicized form of Danish Freya, FREA means "lady, mistress."
Surname or Lastname
English
English : variant spelling of Fry.North German : variant of Frey.Joseph Frye (1711/12–94) was a military officer from Andover, MA, where the family had long been of local prominence. In 1762, he was granted a township in ME, later named Fryeburg after him, and moved his family there. His great-great-grandson William Pierce Frye was born in Lewiston, ME, and served in Congress, first as a member of the House of Representatives and then the Senate from 1871 until his death in 1911.
Boy/Male
Hindu, Indian, Traditional
Content
Surname or Lastname
English
English : nickname from Middle English freil, frel(i)e ‘frail’, ‘weak’.Possibly an Americanized spelling of German Friel 2.
Surname or Lastname
Italian
Italian : from the title of rank conte ‘count’ (from Latin comes, genitive comitis ‘companion’). Probably in this sense (and the Late Latin sense of ‘traveling companion’), it was a medieval personal name; as a title it was no doubt applied ironically as a nickname for someone with airs and graces or simply for someone who worked in the service of a count.English : variant of Count, cognate with 1.French : nickname for someone in the service of a count or for someone who behaved pretentiously, from Old French conte, cunte ‘count’ (of the same derivation as 1).French (Conté) : variant of Comté (see Comte).
Boy/Male
Tamil
Sarnvar | ஸரà¯à®¨à®µà®¾à®°
Content, Best
Sarnvar | ஸரà¯à®¨à®µà®¾à®°
Boy/Male
Tamil
Content
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : nickname or status name from Old English frēo ‘free(-born)’, i.e. not a serf.North German : topographic or habitational name from a place named Frede or Frede(n).North German : nickname from a variant of Middle Low German wrēd ‘crooked’.
Male
English
Short form of English Frederick, FRED means "peaceful ruler."
Male
Icelandic
Icelandic form of Old Norse Freyr, FREY means "lord, master."
Girl/Female
Tamil
Content
Surname or Lastname
English (Devon)
English (Devon) : unexplained.
Male
Swedish
Danish and Swedish form of Old Norse Freyr, FREJ means "lord, master."
Surname or Lastname
English
English : variant of Freer 1.French (Frère) : from frère ‘brother’, used as a byname for the younger of two brothers.
Female
English
English form of Irish BrÃgh, BREE means "force, strength."
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE
CONTEXT FREE-LANGUAGE