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Context-sensitive Grammar
A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by CSG but not by context-free grammars. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSG are positioned between context-free and unrestricted grammars in the Chomsky hierarchy. A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equival ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Visual Programming Language
In computing, a visual programming language (visual programming system, VPL, or, VPS) is any programming language that lets users create programs by manipulating program elements ''graphically'' rather than by specifying them ''textually''. A VPL allows programming with visual expressions, spatial arrangements of text and graphic symbols, used either as elements of syntax or secondary notation. For example, many VPLs (known as ''dataflow'' or ''diagrammatic programming'') are based on the idea of "boxes and arrows", where boxes or other screen objects are treated as entities, connected by arrows, lines or arcs which represent relations. Definition VPLs may be further classified, according to the type and extent of visual expression used, into icon-based languages, form-based languages, and diagram languages. Visual programming environments provide graphical or iconic elements which can be manipulated by users in an interactive way according to some specific spatial grammar for p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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John Myhill
John R. Myhill Sr. (11 August 1923 – 15 February 1987) was a British mathematician. Education Myhill received his Ph.D. from Harvard University under Willard Van Orman Quine in 1949. He was professor at SUNY Buffalo from 1966 until his death in 1987. He also taught at several other universities. His son, also called John Myhill, is a professor of linguistics in the English department of the University of Haifa in Israel. Contributions In the theory of formal languages, the Myhill–Nerode theorem, proven by Myhill with Anil Nerode, characterizes the regular languages as the languages that have only finitely many inequivalent prefixes. In computability theory, the Rice–Myhill–Shapiro theorem, more commonly known as Rice's theorem, states that, for any nontrivial property ''P'' of partial functions, it is undecidable to determine whether a given Turing machine computes a function with property ''P''. The Myhill isomorphism theorem is a computability-theoretic ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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] |
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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] |
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Context-free Language
In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Background Context-free grammar Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language. Automata 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. Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct. Examples An example context-free language is L = \, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Penttonen 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 tec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. Reversal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Noncontracting Grammar
In formal language theory, a grammar is noncontracting (or monotonic) if all of its production rules are of the form α → β where α and β are strings of nonterminal and terminal symbols, and the length of α is less than or equal to that of β, , α, ≤ , β, , that is β is not shorter than α. A grammar is essentially noncontracting if there may be one exception, namely, a rule ''S'' → ε where ''S'' is the start symbol and ε the empty string, and furthermore, ''S'' never occurs in the right-hand side of any rule. None of the rules of a noncontracting grammar decreases the length of the string that is being rewritten. If each rule even properly increases the length, the grammar is called a growing context-sensitive grammar. History Chomsky (1963) called a noncontracting grammar a type 1 grammar; in the same work, he called a context-sensitive grammar a "type 2 grammar", and he proved that these two are weakly equivalent (context-free grammars were desi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Reflexive Transitive Closure
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a ''collection'' of operations if it is closed under each of the operations individually. The closure of a subset is the result of a closure operator applied to the subset. The ''closure'' of a subset under some operations is the smallest subset that is closed under these operations. It is often called the ''span'' (for example linear span) or the ''generated set''. Definitions Let be a set equipped with one or several methods for producing elements of from other elements of .Operations and ( partial) multivariate function are examples of such methods. If is a topological space, the limit of a sequence of elemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Terminal 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] |