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Context-free grammar

Context-free grammar
V → w where V is a single nonterminal symbol, and w is a string of terminals and/or nonterminals (w can be empty). A formal grammar is considered "context free" when its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. Context-free grammars arise in linguistics where they are used to describe the structure of sentences and words in natural language, and they were in fact invented by the Linguist Noam Chomsky for this purpose, but have not really lived up to their original expectation. By contrast, in computer science, as the use of recursively defined concepts increased, they were used more and more. In linguistics, some authors use the term phrase structure grammar to refer to context-free grammars, whereby phrase structure grammars are distinct from dependency grammars. Background[edit] can be logically parenthesized as follows: where Related:  CFDG: Context Free Design Grammar

Kontextfreie Sprache In der Theoretischen Informatik ist eine kontextfreie Sprache (englisch context-free language, CFL) eine formale Sprache, die durch eine kontextfreie Grammatik beschrieben werden kann. Eine kontextfreie Grammatik erlaubt einen definierten Leseprozess (Interpretation) von Ausdrücken einer formalen Sprache. Dabei kann zum einen entschieden werden, ob ein Ausdruck den Regeln der Grammatik entspricht, und zum anderen im Verlauf der Analyse ein Syntaxbaum erstellt werden. Ein Programm, das dies leistet, heißt Parser. Parser werden insbesondere zur Verarbeitung von Programmiersprachen verwendet. Auch in der Computerlinguistik versucht man, natürliche Sprachen durch Regeln kontextfreier Grammatiken zu beschreiben. Kontextfreie Sprachen werden auch als Typ-2-Sprachen der Chomsky-Hierarchie bezeichnet. Man spricht deshalb von kontextfreien Sprachen, weil die Regeln der kontextfreien Grammatiken immer vom Kontext unabhängig angewendet werden. Charakterisierung[Bearbeiten] Beispiele[Bearbeiten] und

Context Free Art – Tutorial 1 » Magic & Love Interactive After we can create different primitive shapes, we start to combine them together. We cannot simply put all the primitive shapes within one single shape rule, like: startshape MyShape rule MyShape { CIRCLE {} TRIANGLE {} SQUARE {} } Multiple shapes Every shape command comes with parameters. startshape MyShape rule MyShape { CIRCLE {x -2} TRIANGLE {} SQUARE {x 2} } startshape MyShape rule MyShape { CIRCLE {y 2} TRIANGLE {} SQUARE {y -2} } startshape MyShape rule MyShape { CIRCLE {x 2 y 2 size 0.8} TRIANGLE {size 2} SQUARE {x -2 y -2 size 0.5} } Size variation Backus–Naur Form In computer science, BNF (Backus Normal Form or Backus–Naur Form) is one of the two[1] main notation techniques for context-free grammars, often used to describe the syntax of languages used in computing, such as computer programming languages, document formats, instruction sets and communication protocols; the other main technique for writing context-free grammars is the van Wijngaarden form. They are applied wherever exact descriptions of languages are needed: for instance, in official language specifications, in manuals, and in textbooks on programming language theory. Many extensions and variants of the original Backus–Naur notation are used; some are exactly defined, including Extended Backus–Naur Form (EBNF) and Augmented Backus–Naur Form (ABNF). History[edit] The idea of describing the structure of language with rewriting rules can be traced back to at least the work of Pāṇini (about the 4th century BC), who used it in his description of Sanskrit word structure. Introduction[edit]

Programming language The earliest programming languages preceded the invention of the digital computer and were used to direct the behavior of machines such as Jacquard looms and player pianos.[1] Thousands of different programming languages have been created, mainly in the computer field, and many more still are being created every year. Many programming languages require computation to be specified in an imperative form (i.e., as a sequence of operations to perform), while other languages utilize other forms of program specification such as the declarative form (i.e. the desired result is specified, not how to achieve it). Definitions[edit] A programming language is a notation for writing programs, which are specifications of a computation or algorithm.[2] Some, but not all, authors restrict the term "programming language" to those languages that can express all possible algorithms.[2][3] Traits often considered important for what constitutes a programming language include: Function and target Abstractions

Linguistic competence Linguistic competence is the system of linguistic knowledge possessed by native speakers of a language. It is in contrast to the concept of Linguistic performance, the way the language system is used in communication. The concept was first introduced by Noam Chomsky[1] as part of the foundations for his Generative Grammar, but it has since been adopted and developed by other linguists, particularly those working in the generativist tradition. In the generativist tradition competence is the only level of language that is studied, because this level gives insights into the Universal Grammar, that generativists see as underlying all human language systems. Functional theories of grammar tend to dismiss the sharp distinction between competence and performance, and particularly the primacy given to the study of competence. Competence versus performance[edit] Chomsky differentiates competence, which is an idealized capacity, from performance being the production of actual utterances. Ray S.

Context-free language In formal language theory, a context-free language (CFL) is a language generated by some context-free grammar (CFG). Different CF grammars can generate the same CF language, or conversely, a given CF language can be generated by different CF grammars. It is important to distinguish properties of the language (intrinsic properties) from properties of a particular grammar (extrinsic properties). The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing. Indeed, given a CFG, there is a direct way to produce a pushdown automaton for the grammar (and corresponding language), though going the other way (producing a grammar given an automaton) is not as direct. Context-free languages have many applications in programming languages; for example, the language of all properly matched parentheses is generated by the grammar . Examples[edit] An archetypical context-free language is 's. where with . The set and

Mathematische Bilder erstellen mit Context Free | vismath In der Blo­grei­he „Wie er­stellt man ma­the­ma­ti­sche Bilder?“ stel­len wir Werk­zeu­ge vor, mit denen man ein­fach hoch­wer­ti­ge ma­the­ma­ti­sche Bilder er­stel­len kann. Dieser Ar­ti­kel be­fasst sich mit dem Pro­gramm Con­text Free und zeigt, wie man damit Ob­jek­te vi­sua­li­sie­ren kann, die über ge­wis­se Er­set­zungs­re­geln de­fi­niert sind. Kontextfreie Grammatiken und Fraktale Con­text Free ist ein Pro­gramm, mit dem man Ob­jek­te zeich­nen kann, die sich über ge­wis­se Re­gel­er­set­zun­gen be­schrei­ben lassen. Ein Bei­spiel für ein ma­the­ma­ti­sches Objekt, das in ganz na­tür­li­cher Weise über solche Er­set­zungs­re­geln er­zeugt werden kann, ist das Sier­pin­ski-Drei­eck. Dann wendet man Re­kur­si­on an, also wie­der­holt die Regel für jedes der klei­nen Drei­ecke. Context Free Art Kennt man ein Objekt, das durch solche Er­set­zungs­re­geln de­fi­niert ist, und möchte davon eine gra­fi­sche Dar­stel­lung er­zeu­gen, kann man nun das Pro­gramm Con­text Free nutzen.

Formal grammar A formal grammar is a set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting results of automata theory is that it is not possible to design a recognizer for certain formal languages. Parsing is the process of recognizing an utterance (a string in natural languages) by breaking it down to a set of symbols and analyzing each one against the grammar of the language. Introductory example[edit] For example, assume the alphabet consists of a and b, the start symbol is S, and we have the following production rules: then we start with S, and can choose a rule to apply to it. . is

Computer science Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations History[edit] The earliest foundations of what would become computer science predate the invention of the modern digital computer. Blaise Pascal designed and constructed the first working mechanical calculator, Pascal's calculator, in 1642.[3] In 1673 Gottfried Leibniz demonstrated a digital mechanical calculator, called the 'Stepped Reckoner'.[4] He may be considered the first computer scientist and information theorist, for, among other reasons, documenting the binary number system. Although many initially believed it was impossible that computers themselves could actually be a scientific field of study, in the late fifties it gradually became accepted among the greater academic population.[15][16] It is the now well-known IBM brand that formed part of the computer science revolution during this time. Misc

Complement (linguistics) In many traditional grammars, the terms subject complement and object complement are employed to denote the predicative expressions (e.g. predicative adjectives and nominals) that serve to assign a property to a subject or object,[3] e.g. Ryan is upset. - Predicative adjective as subject complement Rachelle is the boss. - Predicative nominal as subject complement That made Michael lazy. - Predicative adjective as object complement We call Rachelle the boss. - Predicative nominal as object complement In many modern grammars (for instance in those that build on the X-bar schema), the object argument of a verbal predicate is called a complement. He wiped the counter. - the counter is the object complement of the verb wiped. She scoured the tub. - the tub is the object complement of the verb scoured. The noun phrases (NPs) the counter and the tub are necessary to complete the meaning of the verbs wiped and scoured, respectively, hence they are complements. Borsley, R. 1991.

Context Free Art Context Free Art Context Free Art Context Free is a program that generates images from written instructions called a grammar. This HSV color picker may be useful for color settings. Directives startshape shape A script must start with this directive . Indicates which rule or path is used as the starting point for the generated image. Primitive shapes Context Free knows how to draw squares, circles and triangles. Geometric adjustments A shape passes on its geometry to the shapes that replace it when a rule for the shape is executed. Color adjustments Color adjustments, based on the HSV color model , may also be applied to replacement shapes. Path operations

Related:  Context-Free Grammer