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Nonterminal Symbol
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 language defined by a formal grammar. ''Nonterminal symbols'' (or ''syntactic variables'') are replaced by groups of terminal symbols according to the production rules. The terminals and nonterminals of a particular grammar are two disjoint sets. Terminal symbols Terminal symbols are literal symbols that may appear in the outputs of the production rules of a formal grammar and which cannot be changed using the rules of the grammar. Applying the rules recursively to a source string of symbols will usually terminate in a final output string consisting only of terminal symbols. Consider a grammar defined by two rules. Using pictoric marks interacting with each other: # The symbol ר can become ди # The symbol ר can become д Here д is a terminal symbol because no rule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntactic Structures
''Syntactic Structures'' is an influential work in linguistics by American linguist Noam Chomsky, originally published in 1957. It is an elaboration of his teacher Zellig Harris's model of transformational generative grammar. A short monograph of about a hundred pages, Chomsky's presentation is recognized as one of the most significant studies of the 20th century. It contains the now-famous sentence " Colorless green ideas sleep furiously", which Chomsky offered as an example of a grammatically correct sentence that has no discernible meaning. Thus, Chomsky argued for the independence of syntax (the study of sentence structures) from semantics (the study of meaning).From :"...such semantic notions as reference, significance, and synonymity played no role in the discussion." Based on lecture notes he had prepared for his students at the Massachusetts Institute of Technology, Chomsky's first book presented contemporary developments in early generative grammar. The approach to sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 eventually lead to a string that includes the same non-terminal again. Otherwise it is called a non-recursive grammar.. For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol ''A'' that can be put through the production rules to produce a string with ''A'' (as the leftmost symbol). All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of words. Properties A non-recursive grammar can produce only a finite language; and each finite language can be produced by a non-recursive grammar. For example, a straight-line grammar produces just a single word. A recursive context-free grammar that contains no useless rules necessarily produces an infinite language. This property ... [...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] |
Phrase Structure Grammar
The term phrase structure grammar was originally introduced by Noam Chomsky as the term for grammar studied previously by Emil Post and Axel Thue (Post canonical systems). Some authors, however, reserve the term for more restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars. In a broader sense, phrase structure grammars are also known as ''constituency grammars''. The defining trait of phrase structure grammars is thus their adherence to the constituency relation, as opposed to the dependency relation of dependency grammars. Constituency relation In linguistics, phrase structure grammars are all those grammars that are based on the constituency relation, as opposed to the dependency relation associated with dependency grammars; hence, phrase structure grammars are also known as constituency grammars. Any of several related theories for the parsing of natural language qualify as constituency grammars, and most of them have been develope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rewriting System
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 as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty String
In formal language theory, the empty string, or empty word, is the unique string of length zero. Formal theory Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments, the empty string is denoted with ε or sometimes Λ or λ. The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string. The empty string has several properties: * , ε, = 0. Its string length is zero. * ε ⋅ s = s ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of all strings forms a free monoid with respect to ⋅ and ε. * εR = ε. Reve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union (set Theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of zero (0) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. Union of two sets The union of two sets ''A'' and ''B'' is the set of elements which are in ''A'', in ''B'', or in both ''A'' and ''B''. In set-builder notation, :A \cup B = \. For example, if ''A'' = and ''B'' = then ''A'' ∪ ''B'' = . A more elaborate example (involving two infinite sets) is: : ''A'' = : ''B'' = : A \cup B = \ As another example, the number 9 is ''not'' contained in the union of the set of prime numbers and the set of even numbers , because 9 is neither prime nor even. Sets cannot have duplicate elements, so the union of the sets and is . Multiple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, it is more commonly known as the free monoid construction. The application of the Kleene star to a set V is written as ''V^*''. It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". # If V is a set of strings, then ''V^*'' is defined as the smallest superset of V that contains the empty string \varepsilon and is closed under the string concatenation operation. # If V is a set of symbols or characters, then ''V^*'' is the set of all strings over symbols in V, including the empty string \varepsilon. The set ''V^*'' can also be described as the set containing the empty string and all finite-length strings that can be generated by concatenating arbitrary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjoint Sets
In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set.. For example, and are ''disjoint sets,'' while and are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. Generalizations This definition of disjoint sets can be extended to a family of sets \left(A_i\right)_: the family is pairwise disjoint, or mutually disjoint if A_i \cap A_j = \varnothing whenever i \neq j. Alternatively, some authors use the term disjoint to refer to this notion as well. For families the notion of pairwise disjoint or mutually disjoint is sometimes defined in a subtly different manner, in that repeated identical members are allowed: the family is pairwise disjoint if A_i \cap A_j = \varnothing whenever A_i \neq A_j (every two ''distinct'' sets in the family are disjoint).. For example, the collection of sets is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mouton De Gruyter
Walter de Gruyter GmbH, known as De Gruyter (), is a German scholarly publishing house specializing in academic literature. History The roots of the company go back to 1749 when Frederick the Great granted the Königliche Realschule in Berlin the royal privilege to open a bookstore and "to publish good and useful books". In 1800, the store was taken over by Georg Reimer (1776–1842), operating as the ''Reimer'sche Buchhandlung'' from 1817, while the school’s press eventually became the ''Georg Reimer Verlag''. From 1816, Reimer used the representative Sacken'sche Palace on Berlin's Wilhelmstraße for his family and the publishing house, whereby the wings contained his print shop and press. The building became a meeting point for Berlin salon life and later served as the official residence of the president of Germany. Born in Ruhrort in 1862, Walter de Gruyter took a position with Reimer Verlag in 1894. By 1897, at the age of 35, he had become sole proprietor of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IRE Transactions On Information Theory
''IEEE Transactions on Information Theory'' is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society. It covers information theory and the mathematics of communications. It was established in 1953 as ''IRE Transactions on Information Theory''. The editor-in-chief is Muriel Médard (Massachusetts Institute of Technology). As of 2007, the journal allows the posting of preprints on arXiv. According to Jack van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that, among hundreds of computer science-related journals, ''IEEE Transactions on Information Theory'' had the highest ranking and was thus deemed the most prestigious. ''ACM Computing Surveys'', with the highest impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of cit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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