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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'', or : ''A'' → ''a'', or : ''S'' → ε, where ''A'', ''B'', and ''C'' are nonterminal symbols, the letter ''a'' is a terminal symbol (a symbol that represents a constant value), ''S'' is the start symbol, and ε denotes the empty string. Also, neither ''B'' nor ''C'' may be the start symbol, and the third production rule can only appear if ε is in ''L''(''G''), the language produced by the context-free grammar ''G''. Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent onethat is, one that produces the same language which is in Chomsky normal form and has a size no larger than the square of the original grammar's size. Converting a grammar to Chomsky normal form To convert a grammar to C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or '' well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compiler Front-end
In computing, a compiler is a computer program that Translator (computing), translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a lower level language, low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program.Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different Central processing unit, CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pumping Lemma For Context-free Languages
Pumping may refer to: * The operation of a pump, for moving a liquid from one location to another **The use of a breast pump for extraction of milk * Pumping (audio), a creative misuse of dynamic range compression * Pumping (computer systems), the number of times data is transmitted per clock cycle * Pumping (oil well), injecting chemicals into a wellbore * Pumping (noise reduction), an unwanted artifact of some noise reduction systems * Pumping lemma, in the theory of formal languages * Gastric lavage, cleaning the contents of the stomach * Optical pumping, in which light is used to raise electrons from a lower energy level to a higher one * Pump (skateboarding) {{single source, date=February 2019 Pumping is a skateboarding technique used to accelerate without the rider's feet leaving the board. Pumping can be done by turning or on a transition, like a ramp or quarter pipe.https://skateboarding.transwor ..., accelerating without pushing off of the ground * "Pumping" (My Heart) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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'' or :''A'' → ''BC'' or :''A'' → ''B'' or :''A'' → ''a'' where A, B, C and D are nonterminal symbols and ''a'' is a terminal symbol. Some sources omit the ''A'' → ''B'' pattern. It is named after Sige-Yuki Kuroda, who originally called it a linear bounded grammar—a terminology that was also used by a few other authors thereafter. Every grammar in Kuroda normal form is noncontracting, and therefore, generates a context-sensitive language. Conversely, every context-sensitive language which does not generate the empty string can be generated by a grammar in Kuroda normal form. A straightforward technique attributed to György Révész transforms a grammar in Kuroda's form to Chomsky's CSG: ''AB'' → ''CD'' is replaced by four context-sensitive rules ''AB'' → ''AZ'', ''AZ'' → ''WZ'', ''WZ'' → ''WD'' and ''WD'' → ''CD''. This te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name. More precisely, a context-free grammar is in Greibach normal form, if all production rules are of the form: :A \to a A_1 A_2 \cdots A_n where A is a nonterminal symbol, a is a terminal symbol, A_1 A_2 \ldots A_n is a (possibly empty) sequence of nonterminal symbols not including the start symbol and S is the start symbol. Observe that the grammar does not have left recursions. Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form. Various constructions exist. Some do not permit the second form of rule and cannot transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bottom-up Parsing
In computer science, parsing reveals the grammatical structure of linear input text, as a first step in working out its meaning. Bottom-up parsing recognizes the text's lowest-level small details first, before its mid-level structures, and leaving the highest-level overall structure to last. Bottom-up Versus Top-down The bottom-up name comes from the concept of a parse tree, in which the most detailed parts are at the bottom of the upside-down tree, and larger structures composed from them are in successively higher layers, until at the top or "root" of the tree a single unit describes the entire input stream. A bottom-up parse discovers and processes that tree starting from the bottom left end, and incrementally works its way upwards and rightwards. Compilers: Principles, Techniques, and Tools (2nd Edition), by Alfred Aho, Monica Lam, Ravi Sethi, and Jeffrey Ullman, Prentice Hall 2006. A parser may act on the structure hierarchy's low, mid, and highest levels without ever c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CYK Algorithm
In computer science, the Cocke–Younger–Kasami 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 some of its rediscoverers: John Cocke, Daniel Younger, Tadao Kasami, and Jacob T. Schwartz. It employs bottom-up parsing and dynamic programming. The standard version of CYK operates only on context-free grammars given in Chomsky normal form (CNF). However any context-free grammar may be transformed (after convention) to a CNF grammar expressing the same language . The importance of the CYK algorithm stems from its high efficiency in certain situations. Using big ''O'' notation, the worst case running time of CYK is \mathcal\left( n^3 \cdot \left, G \ \right), where n is the length of the parsed string and \left, G \ is the size of the CNF grammar G . This makes it one of the most efficient parsing algorithms in terms of worst-case asymptotic complexity, although other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert W
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald E
Donald is a masculine given name derived from the Gaelic name ''Dòmhnall''.. This comes from the Proto-Celtic *''Dumno-ualos'' ("world-ruler" or "world-wielder"). The final -''d'' in ''Donald'' is partly derived from a misinterpretation of the Gaelic pronunciation by English speakers, and partly associated with the spelling of similar-sounding Germanic names, such as ''Ronald''. A short form of ''Donald'' is ''Don''. Pet forms of ''Donald'' include ''Donnie'' and ''Donny''. The feminine given name ''Donella'' is derived from ''Donald''. ''Donald'' has cognates in other Celtic languages: Modern Irish ''Dónal'' (anglicised as ''Donal'' and ''Donall'');. Scottish Gaelic ''Dòmhnall'', ''Domhnull'' and ''Dòmhnull''; Welsh '' Dyfnwal'' and Cumbric ''Dumnagual''. Although the feminine given name '' Donna'' is sometimes used as a feminine form of ''Donald'', the names are not etymologically related. Variations Kings and noblemen Domnall or Domhnall is the name of many a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backus–Naur Form
In computer science, Backus–Naur form () or Backus normal form (BNF) is a metasyntax notation 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. It is 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). Overview A BNF specification is a set of derivation rules, written as ::= __expression__ where: * is a '' nonterminal'' (variable) and the __expression__ consists of one or more sequences of either terminal or nonterminal symbols; * means that the symbol on the left must be replaced with the expression on the right. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. 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 det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converting A Grammar To Chomsky Normal Form
Converting companies are companies that specialize in modifying or combining raw materials such as polyesters, adhesives, silicone, adhesive tapes, foams, plastics, felts, rubbers, liners and metals, as well as other materials, to create new products. Materials such as paper, plastic film, foil and cloth often are produced in long, continuous sheets that are rolled up for more convenient handling and transportation. These rolls of material vary significantly in size and weight — ranging from wide and weighing as much as several tons. The converting industry takes these continuous rolls of thin, flat materials — known as webs — threads them through processing machines (such as printing presses, laminating, coating and slitting machines) and converts or changes the web of material into an intermediate form or final product. For example, a converter’s equipment might take a web of plastic film, cut it into lengths, and fuse their edges, thus converting it into plastic bag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
