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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 Grammarlanguages

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]

Regular language In theoretical computer science and formal language theory, a regular language is a formal language that can be expressed using a regular expression. (Note that the "regular expression" features provided with many programming languages are augmented with features that make them capable of recognizing languages that can not be expressed by the formal regular expressions (as formally defined below).) Alternatively, a regular language can be defined as a language recognized by a finite automaton. In the Chomsky hierarchy, regular languages are defined to be the languages that are generated by Type-3 grammars (regular grammars). Regular languages are very useful in input parsing and programming language design. Formal definition[edit] The collection of regular languages over an alphabet Σ is defined recursively as follows: See regular expression for its syntax and semantics. Examples All finite languages are regular; in particular the empty string language {ε} = Ø* is regular. then the set . Let in

Chomsky Hierarchy 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

Hack prerequisite for a 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