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Nonterminal
In formal languages, terminal and nonterminal symbols are parts of the ''vocabulary'' under a formal grammar. ''Vocabulary'' is a finite, nonempty set of symbols. ''Terminal symbols'' are symbols that cannot be replaced by other symbols of the vocabulary. ''Nonterminal symbols'' are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar. A formal grammar defines a formal language over the vocabulary of the grammar. In the context of formal language, the term ''vocabulary'' is more commonly known as ''alphabet''. Nonterminal symbols are also called ''syntactic variables''. Terminal symbols Terminal symbols are those symbols that can appear in the formal language defined by a formal grammar. The process of applying the production rules successively to a start symbol might not terminate, but if it terminates when there is no more production rule can be applied, the output string will consist only of terminal symb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form : A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). Regardless of which symbols surround it, the single nonterminal A on the left hand side can always be replaced by \alpha on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form \alpha A \beta \rightarrow \alpha \gamma \beta with A a nonterminal symbol and \alpha, \beta, and \gamma strings of terminal and/or nonterminal symbols. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, : \lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabet. A grammar does not describe the semantics, meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, Formal semantics (logic), formal semantics, mathematical logic, and other areas. A formal grammar is a Set_(mathematics), 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 grammatical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky Hierarchy
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a formal language's alphabet that are valid according to the language's syntax. The linguist Noam Chomsky theorized that four different classes of formal grammars existed that could generate increasingly complex languages. Each class can also completely generate the language of all inferior classes (set inclusive). History The general idea of a hierarchy of grammars was first described by Noam Chomsky in "Three models for the description of language" during the formalization of transformational-generative grammar (TGG). Marcel-Paul Schützenberger also played a role in the development of the theory of formal languages; the paper "The algebraic theory of context free languages" describes the modern hierarchy, including context-free grammars. Independently, alongside linguis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Push Down Automaton
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Production (computer Science)
In computer science, a production or production rule is a rewrite rule that replaces some symbols with other symbols. A finite set of productions P is the main component in the specification of a formal grammar (specifically a generative grammar). The other components are a finite set N of nonterminal symbols, a finite set (known as an alphabet) \Sigma of terminal symbols that is disjoint from N and a distinguished symbol S \in N that is the ''start symbol''. In an unrestricted grammar, a production is of the form u \to v, where u and v are arbitrary strings of terminals and nonterminals, and u may not be the empty string. If v is the empty string, this is denoted by the symbol \epsilon, or \lambda (rather than leaving the right-hand side blank). So productions are members of the cartesian product :V^*NV^* \times V^* = (V^*\setminus\Sigma^*) \times V^*, where V := N \cup \Sigma is the ''vocabulary'', ^ is the Kleene star operator, V^*NV^* indicates concatenation, \cup deno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminal And Non-terminal Symbols Example
Terminal may refer to: Computing Hardware * Computer terminal, a set of primary input and output devices for a computer * Terminal (electronics), a device for joining electrical circuits together ** Battery terminal, electrical contact used to connect a load or charger to a single cell or multiple-cell battery * Terminal (telecommunication), a device communicating over a line * Feedback terminal, a physical device used collect anonymous feedback Software * Terminal emulator, a program that emulates a computer terminal within some other display architecture ** Terminal (macOS), a terminal emulator included with macOS ** Windows Terminal, a terminal emulator for Windows 10 and Windows 11 ** GNOME Terminal, a Linux and BSD terminal emulator * Terminal and nonterminal symbols, lexical elements used in specifying the production rules constituting a formal grammar in computer science. Fonts * Terminal (typeface), a monospace font * Terminal (typography), a type of stroke ending Trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabet (formal Languages)
In formal language theory, an alphabet, sometimes called a vocabulary, is a non-empty set of indivisible symbols/ characters/glyphs, typically thought of as representing letters, characters, digits, phonemes, or even words. The definition is used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and, depending on its purpose, may be finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., \), or even uncountable (e.g., \). Strings, also known as "words" or "sentences", over an alphabet are defined as a sequence of the symbols from the alphabet set. For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is , the binary alphabet, and a "00101111" is an example of a binary string. Infinite sequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backus–Naur Form
In computer science, Backus–Naur form (BNF, pronounced ), also known as Backus normal form, is a notation system for defining the Syntax (programming languages), syntax of Programming language, programming languages and other Formal language, formal languages, developed by John Backus and Peter Naur. It is a metasyntax for Context-free grammar, context-free grammars, providing a precise way to outline the rules of a language's structure. It has been widely used in official specifications, manuals, and textbooks on programming language theory, as well as to describe Document format, document formats, Instruction set, instruction sets, and Communication protocol, communication protocols. Over time, variations such as extended Backus–Naur form (EBNF) and augmented Backus–Naur form (ABNF) have emerged, building on the original framework with added features. Structure BNF specifications outline how symbols are combined to form syntactically valid sequences. Each BNF consists of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminal And Non-terminal Symbols Example Number Two
Terminal may refer to: Computing Hardware * Computer terminal, a set of primary input and output devices for a computer * Terminal (electronics), a device for joining electrical circuits together ** Battery terminal, electrical contact used to connect a load or charger to a single cell or multiple-cell battery * Terminal (telecommunication), a device communicating over a line * Feedback terminal, a physical device used collect anonymous feedback Software * Terminal emulator, a program that emulates a computer terminal within some other display architecture ** Terminal (macOS), a terminal emulator included with macOS ** Windows Terminal, a terminal emulator for Windows 10 and Windows 11 ** GNOME Terminal, a Linux and BSD terminal emulator * Terminal and nonterminal symbols, lexical elements used in specifying the production rules constituting a formal grammar in computer science. Fonts * Terminal (typeface), a monospace font * Terminal (typography), a type of stroke ending T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleene Star
In mathematical logic and theoretical computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation on a Set (mathematics), set to generate a set of all finite-length strings that are composed of zero or more repetitions of members from . It was named after American mathematician Stephen Cole Kleene, who first introduced and widely used it to characterize Automata theory, automata for regular expressions. In mathematics, it is more commonly known as the free monoid construction. Definition Given a set V, define :V^=\ (the set consists only of the empty string), :V^=V, and define recursively the set :V^=\ for each i>0. V^i is called the i-th power of V, it is a shorthand for the Concatenation#Concatenation of sets of strings, concatenation of V by itself i times. That is, ''V^i'' can be understood to be the set of all strings that can be represented as the concatenation of i members from V. The definition of Kleene star on V is : V^*=\bigcup_V^i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
