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- Formal languages

Parser combinator

In computer programming, a parser combinator is a higher-order function that accepts several parsers as input and returns a new parser as its output. In this context, a parser is a function accepting

Semantics encoding

A semantics encoding is a translation between formal languages. For programmers, the most familiar form of encoding is the compilation of a programming language into machine code or byte-code. Convers

Cyclic language

In computer science, more particularly in formal language theory, a cyclic language is a set of strings that is closed with respect to repetition, root, and cyclic shift.

Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic te

Proof (truth)

A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines,with both the nature of the evidence or justification and the cr

Abstract family of acceptors

An abstract family of acceptors (AFA) is a grouping of generalized acceptors. Informally, an acceptor is a device with a finite state control, a finite number of input symbols, and an internal store w

Context-free language

In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular,

Trace monoid

In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters t

Tree automaton

A tree automaton is a type of state machine. Tree automata deal with tree structures, rather than the strings of more conventional state machines. The following article deals with branching tree autom

Cross-serial dependencies

In linguistics, cross-serial dependencies (also called crossing dependencies by some authors) occur when the lines representing the dependency relations between two series of words cross over each oth

Conjunctive grammar

Conjunctive grammars are a class of formal grammarsstudied in formal language theory.They extend the basic type of grammars,the context-free grammars,with a conjunction operation.Besides explicit conj

Descriptional Complexity of Formal Systems

DCFS, the International Workshop on Descriptional Complexity of Formal Systems is an annual academic conference in the field of computer science. Beginning with the 2011 edition, the proceedings of th

Muller–Schupp theorem

In mathematics, the Muller–Schupp theorem 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 Sch

Terminal yield

In formal language theory, the terminal yield (or fringe) of a tree is the sequence of leaves encountered in an ordered walk of the tree. Parse trees and/or derivation trees are encountered in the stu

Substring

In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "the best of" is a substring of "It was the best of times". In contras

Autocorrelation (words)

In combinatorics, a branch of mathematics, the autocorrelation of a word is the set of periods of this word. More precisely, it is a sequence of values which indicate how much the end of a word looks

Kuroda normal form

In formal language theory, a context-sensitive grammar is in Kuroda normal form if all production rules are of the form: AB → CD orA → BC orA → B orA → a where A, B, C and D are nonterminal symbols an

Signed-digit representation

In mathematical notation for numbers, a signed-digit representation is a positional numeral system with a set of signed digits used to encode the integers. Signed-digit representation can be used to a

L-attributed grammar

L-attributed grammars are a special type of attribute grammars. They allow the attributes to be evaluated in one depth-first left-to-right traversal of the abstract syntax tree. As a result, attribute

LL 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 a Leftmost derivation of the sentence (

Left recursion

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 th

Regular expression

A regular expression (shortened as regex or regexp; sometimes referred to as rational expression) is a sequence of characters that specifies a search pattern in text. Usually such patterns are used by

Linear grammar

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 language is a language generated by some li

Emptiness problem

In theoretical computer science and formal language theory, a formal language is empty if its set of valid sentences is the empty set. The emptiness problem is the question of determining whether a la

Parikh's theorem

Parikh's theorem in theoretical computer science says that if one looks only at the number of occurrences of each terminal symbol in a context-free language, without regard to their order, then the la

Chomsky normal form

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 are of the form: A → BC, orA → a, orS → ε, w

Minimalist grammar

Minimalist grammars are a class of formal grammars that aim to provide a more rigorous, usually proof-theoretic, formalization of Chomskyan Minimalist program than is normally provided in the mainstre

Two-level grammar

A two-level grammar is a formal grammar that is used to generate another formal grammar [1], such as one with an infinite rule set [2]. This is how a Van Wijngaarden grammar was used to specify Algol

Free monoid

In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid ope

Language identification in the limit

Language identification in the limit is a formal model for inductive inference of formal languages, mainly by computers (see machine learning and induction of regular languages). It was introduced by

Turing machine

A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is

Induction of regular languages

In computational learning theory, induction of regular languages refers to the task of learning a formal description (e.g. grammar) of a regular language from a given set of example strings. Although

Categorial grammar

Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a cl

Regulated rewriting

Regulated rewriting is a specific area of formal languages studying grammatical systems which are able to take some kind of control over the production applied in a derivation step. For this reason, t

Growing context-sensitive grammar

In formal language theory, a growing context-sensitive grammar is a context-sensitive grammar in which the productions increase the length of the sentences being generated. These grammars are thus non

Matrix grammar

A matrix grammar is a formal grammar in which instead of single productions, productions are grouped together into finite sequences. A production cannot be applied separately, it must be applied in se

Extended affix grammar

In computer science, extended affix grammars (EAGs) are a formal grammar formalism for describing the context free and context sensitive syntax of language, both natural language and programming langu

Smallest grammar problem

In data compression and the 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 (but no oth

Free partially commutative group

No description available.

Shamir congruence

No description available.

Empty string

In formal language theory, the empty string, or empty word, is the unique string of length zero.

Pumping lemma for regular languages

In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long stri

Semi-Thue system

In theoretical computer science and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a (usually finite) alphabet. Giv

Van Wijngaarden grammar

In computer science, a Van Wijngaarden grammar (also vW-grammar or W-grammar) is a two-level grammar which provides a technique to define potentially infinite context-free grammars in a finite number

Markup language

Markup language refers to a text-encoding system consisting of a set of symbols inserted in a text document to control its structure, formatting, or the relationship between its parts. Markup is often

Prefix grammar

In theoretical computer science and formal language theory, a prefix grammar is a type of string rewriting system, consisting of a set of string rewriting rules, and similar to a formal grammar or a s

Probabilistic context-free grammar

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

Stochastic language

No description available.

Parsing expression grammar

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. Th

Simple precedence grammar

A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser. The concept was first created in 1964 by Claude Pair, and was later rediscovered, from

Abstract rewriting system

In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism that captures the qui

Syntax (logic)

In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructin

Deterministic context-free grammar

In formal grammar theory, the deterministic context-free grammars (DCFGs) are a proper subset of the context-free grammars. They are the subset of context-free grammars that can be derived from determ

Unary language

In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1k, where "1" can be any fixed symbol. For example, the l

Ambiguous 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 parse tree, while an unambiguous grammar is a con

Hall word

In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on th

SCIgen

SCIgen is a paper generator that uses context-free grammar to randomly generate nonsense in the form of computer science research papers. Its original data source was a collection of computer science

Affix grammar

An affix grammar is a kind of formal grammar; it is used to describe the syntax of languages, mainly computer languages, using an approach based on how natural language is typically described. The gra

Straight-line grammar

A straight-line grammar (sometimes abbreviated as SLG) is a formal grammar that generates exactly one string. Consequently, it does not branch (every non-terminal has only one associated production ru

Top-down parsing language

Top-Down Parsing Language (TDPL) is a type of analytic formal grammar developed by in the early 1970s in order to study formally the behavior of a common class of practical top-down parsers that suppo

Unavoidable pattern

In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet.

Büchi-Elgot-Trakhtenbrot theorem

In formal language theory, the Büchi-Elgot-Trakhtenbrot theorem states that a language is regular if and only if it can be defined in monadic second-order logic (MSO): for every MSO formula, we can fi

Context-free grammar

In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form with a single nonterminal symbol, and a string of terminals and/or nonterminals ( can

Longest increasing subsequence

In computer science, the longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which th

Operator-precedence grammar

An 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 (among others)that no production h

Star height

In theoretical computer science, more precisely in the theory of formal languages, the star height is a measure for the structural complexity of regular expressions and regular languages. The star hei

Algorithmic learning theory

Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory and algorithmic inductive inference. Algorithmic

Rewriting

In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known

Parser Grammar Engine

The Parser Grammar Engine (PGE, originally the Parrot Grammar Engine) is a compiler and runtime for Raku rules for the Parrot virtual machine. PGE uses these rules to convert a parsing expression gram

Pumping lemma for context-free languages

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 that gives a property shared by all context-f

Sparse language

In computational complexity theory, a sparse language is a formal language (a set of strings) such that the complexity function, counting the number of strings of length n in the language, is bounded

Abstract syntax tree

In computer science, an abstract syntax tree (AST), or just syntax tree, is a tree representation of the abstract syntactic structure of text (often source code) written in a formal language. Each nod

Profinite word

In mathematics, more precisely in formal language theory, the profinite words are a generalization of the notion of finite words into a complete topological space. This notion allows the use of topolo

Metacharacter

A metacharacter is a character that has a special meaning to a computer program, such as a shell interpreter or a regular expression (regex) engine. In POSIX extended regular expressions, there are 14

Non-logical symbol

In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical

Quotient of a formal language

In mathematics and computer science, the right quotient (or simply quotient) of a language with respect to language is the language consisting of strings w such that wx is in for some string x in . Fo

Deterministic context-free language

In formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are the context-free languages that can be accepted by a deterministic pushdo

Closest string

In theoretical computer science, the closest string is an NP-hard computational problem, which tries to find the geometrical center of a set of input strings. To understand the word "center", it is ne

Symbol (formal)

A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some ti

Regular numerical predicate

In computer science and mathematics, more precisely in automata theory, model theory and formal language, a regular numerical predicate is a kind of relation over integers. Regular numerical predicate

Star height problem

The star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of

Concatenation

In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In

Morphic word

In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automat

LR-attributed grammar

LR-attributed grammars are a special type of attribute grammars. They allow the attributes to be evaluated on LR parsing. As a result, attribute evaluation in LR-attributed grammars can be incorporate

Arden's rule

In theoretical computer science, Arden's rule, also known as Arden's lemma, is a mathematical statement about a certain form of language equations.

Ranked alphabet

In theoretical computer science and formal language theory, a ranked alphabet is a pair of an ordinary alphabet F and a function Arity: F→. Each letter in F has its arity so it can be used to build te

Set constraint

In mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms.Similar to systems of (in)equations between numbers, methods are studied for sol

Augmented Backus–Naur form

In computer science, augmented Backus–Naur form (ABNF) is a metalanguage based on Backus–Naur form (BNF), but consisting of its own syntax and derivation rules. The motive principle for ABNF is to des

Equivalence problem

In theoretical computer science and formal language theory, the equivalence problem is the question of determining, given two representations of formal languages, whether they denote the same formal l

Quasi-quotation

Quasi-quotation or Quine quotation is a linguistic device in formal languages that facilitates rigorous and terse formulation of general rules about linguistic expressions while properly observing the

Attribute grammar

An attribute grammar is a formal way to supplement a formal grammar with semantic information processing. Semantic information is stored in attributes associated with terminal and nonterminal symbols

Gesture Description Language

Gesture Description Language (GDL or GDL Technology) is a method of describing and automatic (computer) syntactic classification of gestures and movements createdby doctor Tomasz Hachaj (PhD) and prof

Unrestricted grammar

In automata theory, the class of unrestricted grammars (also called semi-Thue, type-0 or phrase structure grammars) is the most general class of grammars in the Chomsky hierarchy. No restrictions are

Kleene algebra

In mathematics, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operat

Regular grammar

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

Range concatenation grammar

Range concatenation grammar (RCG) is a grammar formalism developed by Pierre Boullier in 1998 as an attempt to characterize a number of phenomena of natural language, such as Chinese numbers and Germa

Generalized context-free grammar

Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition functions to rewrite rules. Head grammar (and it

Introduction to Automata Theory, Languages, and Computation

Introduction to Automata Theory, Languages, and Computation is an influential computer science textbook by John Hopcroft and Jeffrey Ullman on formal languages and the theory of computation. Rajeev Mo

Maximal pair

In computer science, a maximal pair within a string is a pair of matching substrings that are maximal, where "maximal" means that it is not possible to make a longer matching pair by extending the ran

String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length ch

Discontinuous-constituent phrase structure grammar

Discontinuous-constituent Phrase Structure Grammar (DCPSG) (distinct from Discontinuous Phrase Structure Grammar/DPSG) is a formalism for describing discontinuous phrase structures in natural language

Locally catenative sequence

In mathematics, a locally catenative sequence is a sequence of words in which each word can be constructed as the concatenation of previous words in the sequence. Formally, an infinite sequence of wor

Action algebra

In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to

Splicing rule

In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language genera

Greibach's theorem

In theoretical computer science, in particular in formal language theory, Greibach's theorem states that certain properties of formal language classes are undecidable. It is named after the computer s

Regular tree grammar

In theoretical computer science and formal language theory, a regular tree grammar is a formal grammar that describes a set of directed trees, or terms. A regular word grammar can be seen as a special

Myhill–Nerode theorem

In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who prove

Grammar systems theory

Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-calle

Omega language

In formal language theory within theoretical computer science, an infinite word is an infinite-length sequence (specifically, an ω-length sequence) of symbols, and an ω-language is a set of infinite w

Tree transducer

In theoretical computer science and formal language theory, a tree transducer (TT) is an abstract machine taking as input a tree, and generating output – generally other trees, but models producing wo

Normal form (abstract rewriting)

In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or no

Local language (formal language)

In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word

Formal grammar

In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the

Recurrent word

In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquip

Unary numeral system

The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times. In the unary system, the number 0 (zero) is

Diff

In computing, the utility diff is a data comparison tool that computes and displays the differences between the contents of files. Unlike edit distance notions used for other purposes, diff is line-or

Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part

Recursive grammar

In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventuall

Mildly context-sensitive grammar formalism

In computational linguistics, the term mildly context-sensitive grammar formalisms refers to several grammar formalisms that have been developed in an effort to provide adequate descriptions of the sy

Formal language

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. The alp

Lexical grammar

In computer science, a lexical grammar is a formal grammar defining the syntax of tokens. The program is written using characters that are defined by the lexical structure of the language used. The ch

Leftist grammar

In formal language theory, a leftist grammar is a formal grammar on which certain restrictions are made on the left and right sides of the grammar's productions. Only two types of productions are allo

History monoid

In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individ

Antimatroid

In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remain

Compiler Description Language

Compiler Description Language (CDL) is a programming language based on affix grammars. It is very similar to Backus–Naur form (BNF) notation. It was designed for the development of compilers. It is ve

Syntax diagram

Syntax diagrams (or railroad diagrams) are a way to represent a context-free grammar. They represent a graphical alternative to Backus–Naur form, EBNF, Augmented Backus–Naur form, and other text-based

Conference on Implementation and Application of Automata

CIAA, the International Conference on Implementation and Application of Automata is an annual academic conference in the field of computer science. Its purpose is to bring together members of the acad

Compact semigroup

In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on t

S-attributed grammar

S-attributed grammars are a class of attribute grammars characterized by having no inherited attributes, but only synthesized attributes. Inherited attributes, which must be passed down from parent no

Context-sensitive grammar

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. Cont

Deterministic pushdown automaton

In automata theory, a deterministic pushdown automaton (DPDA or DPA) is a variation of the pushdown automaton. The class of deterministic pushdown automata accepts the deterministic context-free langu

Star-free language

A regular language is said to be star-free if it can be described by a regular expression constructed from the letters of the alphabet, the empty set symbol, all boolean operators – including compleme

Formation rule

In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only add

Alphabet (formal languages)

In formal language theory, an alphabet is a non-empty set of symbols/glyphs, typically thought of as representing letters, characters, or digits but among other possibilities the "symbols" could also

Cone (formal languages)

In formal language theory, a cone is a set of formal languages that has some desirable closure properties enjoyed by some well-known sets of languages, in particular by the families of regular languag

Longest repeated substring problem

In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space

Extended Backus–Naur form

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 fo

Formal proof

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or fo

Nested word

In computer science, more specifically in automata and formal language theory, nested words are a concept proposed by Alur and Madhusudan as a joint generalization of words, as traditionally used for

Greibach normal form

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.

Critical exponent of a word

In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number of times a contiguous subsequence can be repe

List of formal language and literal string topics

This is a list of formal language and literal string topics, by Wikipedia page.

Chomsky hierarchy

In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars.

Kleene star

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics,i

Noncontracting grammar

In formal language theory, a grammar is noncontracting (or monotonic) if all of its production rules are of the form α → β where α and β are strings of nonterminal and terminal symbols, and the length

Monoid factorisation

In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the sub

Recursively enumerable language

In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it i

Picture language

In formal language theory, a picture language is a set of pictures, where a picture is a 2D array of characters over some alphabet. For example, the language defines the language of rectangles compose

WFF 'N PROOF

WFF 'N PROOF is a game of modern logic, developed to teach principles of symbolic logic. It was developed by Layman E. Allen in 1962 a former professor of Yale Law School and the University of Michiga

Head grammar

Head grammar (HG) is a grammar formalism introduced in Carl Pollard (1984) as an extension of the context-free grammar class of grammars. Head grammar is therefore a type of phrase structure grammar,

Literal movement grammar

In linguistics and theoretical computer science, literal movement grammars (LMGs) are a grammar formalism intended to characterize certain extraposition phenomena of natural language such as topicaliz

Chomsky–Schützenberger representation theorem

In formal language theory, the Chomsky–Schützenberger representation theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about representing a given context-free language in ter

ECLR-attributed grammar

ECLR-attributed grammars are a special type of attribute grammars. They are a variant of LR-attributed grammars where an equivalence relation on inherited attributes is used to optimize attribute eval

Global index grammar

Global index grammars (GIGs) are a class of grammars introduced in Castaño (2004) in order to model a number of phenomena, including natural language grammar and genome grammar. The easiest descriptio

Agent Communications Language

Agent Communication Language (ACL), proposed by the Foundation for Intelligent Physical Agents (FIPA), is a proposed standard language for agent communications. Knowledge Query and Manipulation Langua

SLR grammar

SLR grammars are the class of formal grammars accepted by a Simple LR parser. SLR grammars are a superset of all LR(0) grammars and a subset of all LALR(1) and LR(1) grammars. When processed by an SLR

Shortest common supersequence problem

In computer science, the shortest common supersequence of two sequences X and Y is the shortest sequence which has X and Y as subsequences. This is a problem closely related to the longest common subs

String operations

In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used for computer programming, and

Syntactic predicate

A syntactic predicate specifies the syntactic validity of applying a production in a formal grammar and is analogous to a semantic predicate that specifies the semantic validity of applying a producti

Terminal and nonterminal symbols

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

Abstract semantic graph

In computer science, an abstract semantic graph (ASG) or term graph is a form of abstract syntax in which an expression of a formal or programming language is represented by a graph whose vertices are

Equivalence (formal languages)

In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is disti

Recursive language

In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possi

Montague grammar

Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate lo

Definite clause grammar

A definite clause grammar (DCG) is a way of expressing grammar, either for natural or formal languages, in a logic programming language such as Prolog. It is closely related to the concept of attribut

Regular language

In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense i

Indexed grammar

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

Syntactic monoid

In mathematics and computer science, the syntactic monoid of a formal language is the smallest monoid that recognizes the language .

Tree (automata theory)

In automata theory, a tree is a particular way of representing a tree structure as sequences of natural numbers. For example, each node of the tree is a word over set of natural numbers, which helps t

Abstract family of languages

In computer science, in particular in the field of formal language theory,an abstract family of languages is an abstract mathematical notion generalizing characteristics common to the regular language

Brzozowski derivative

In theoretical computer science, in particular in formal language theory, the Brzozowski derivative of a set of strings and a string is the set of all strings obtainable from a string in by cutting of

Pattern language (formal languages)

In theoretical computer science, a pattern language is a formal language that can be defined as the set of all particular instances of a string of constants and variables. Pattern Languages were intro

Bigram

A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every

Controlled grammar

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 co

Backus–Naur form

In computer science, Backus–Naur form (/ˌbækəs ˈnaʊər/) or Backus normal form (BNF) is a metasyntax notation for context-free grammars, often used to describe the syntax of languages used in computing

Ogden's lemma

In the theory of formal languages, Ogden's lemma (named after ) is a generalization of the pumping lemma for context-free languages.

International Conference on Developments in Language Theory

DLT, the International Conference on Developments in Language Theory is an academic conference in the field of computer scienceheld annually under the auspices of the European Association for Theoreti

Context-sensitive language

In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the

Generalized star-height problem

The generalized star-height problem in formal language theory is the open question whether all regular languages can be expressed using generalized regular expressions with a limited nesting depth of

Indexed language

Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata. Indexed languages are a proper subset

Trace theory

In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an a

Production (computer science)

A production or production rule in computer science is a rewrite rule specifying a symbol substitution that can be recursively performed to generate new symbol sequences. A finite set of productions i

Dyck language

In the theory of formal languages of computer science, mathematics, and linguistics, a Dyck word is a balanced string of square brackets [ and ]. The set of Dyck words forms the Dyck language. Dyck wo

Adaptive grammar

An adaptive grammar is a formal grammar that explicitly provides mechanisms within the formalism to allow its own production rules to be manipulated.

Post canonical system

A Post canonical system, also known as a Post production system, as created by Emil Post, is a string-manipulation system that starts with finitely-many strings and repeatedly transforms them by apply

Wirth–Weber precedence relationship

In computer science, a Wirth–Weber relationship between a pair of symbols is necessary to determine if a formal grammar is a simple precedence grammar. In such a case, the simple precedence parser can

Dershowitz–Manna ordering

In mathematics, the Dershowitz–Manna ordering is a well-founded ordering on multisets named after Nachum Dershowitz and Zohar Manna. It is often used in context of termination of programs or term rewr

Junction Grammar

Junction Grammar is a descriptive model of language developed during the 1960s by (1936–2010)[14]. Junction Grammar is based on the premise that the meaning of language can be described and precisely

Omega-regular language

The ω-regular languages are a class of ω-languages that generalize the definition of regular languages to infinite words.

Synchronous context-free 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 machine translation. Rules in these grammars

Dyck congruence

No description available.

Chomsky–Schützenberger enumeration theorem

In formal language theory, the Chomsky–Schützenberger enumeration theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about the number of words of a given length generated by a

Rational series

In mathematics and computer science, a rational series is a generalisation of the concept of formal power series over a ring to the case when the basic algebraic structure is no longer a ring but a se

Boolean grammar

Boolean grammars, introduced by , are a class of formal grammars studied in formal language theory. They extend the basic type of grammars, the context-free grammars, with conjunction and negation ope

Formal system

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 th

Sesquipower

In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix. Sesquipowers are unavoidable patterns, in the sense that all sufficiently long strings contai

Language equation

Language equations are mathematical statements that resemble numerical equations, but the variables assume values of formal languages rather than numbers. Instead of arithmetic operations in numerical

Finite thickness

In formal language theory, in particular in algorithmic learning theory, a class C of languages has finite thickness if every string is contained in at most finitely many languages in C. This conditio

Descriptive interpretation

According to Rudolf Carnap, in logic, an interpretation is a descriptive interpretation (also called a factual interpretation) if at least one of the undefined symbols of its formal system becomes, in

Interchange lemma

In the theory of 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. It states that for ever

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