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Chomsky Hierarchy
In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. Formal grammars A formal grammar of this type consists of a finite set of '' production rules'' (''left-hand side'' → ''right-hand side''), where each side consists of a finite sequence of the following symbols: * a finite set of '' nonterminal symbols'' (indicating that some production rule can yet be applied) * a finite set of ''terminal symbols'' (indicating that no production rule can be applied) * a ''start symbol'' (a distinguished nonterminal symbol) A formal grammar provides an axiom schema for (or ''generates'') a ''formal language'', which is a (usually infinite) ... [...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] |
Natural Language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages can take different forms, such as speech or signing. They are distinguished from constructed and formal languages such as those used to program computers or to study logic. Defining natural language Natural language can be broadly defined as different from * artificial and constructed languages, e.g. computer programming languages * constructed international auxiliary languages * non-human communication systems in nature such as whale and other marine mammal vocalizations or honey bees' waggle dance. All varieties of world languages are natural languages, including those that are associated with linguistic prescriptivism or language regulation. ( Nonstandard dialects can be viewed as a wild type in comparison with stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite State Automaton
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Grammar
In theoretical computer science and formal language theory, a regular grammar is a grammar that is ''right-regular'' or ''left-regular''. While their exact definition varies from textbook to textbook, they all require that * all production rules have at most one non-terminal symbol; * that symbol is either always at the end or always at the start of the rule's right-hand side. Every regular grammar describes a regular language. Strictly regular grammars A right-regular grammar (also called right-linear grammar) is a formal grammar (''N'', Σ, ''P'', ''S'') in which all production rules in ''P'' are of one of the following forms: # ''A'' → ''a'' # ''A'' → ''aB'' # ''A'' → ε where ''A'', ''B'', ''S'' ∈ ''N'' are non-terminal symbols, ''a'' ∈ Σ is a terminal symbol, and ε denotes the empty string, i.e. the string of length 0. ''S'' is called the start symbol. In a left-regular grammar, (also called left-linear grammar), all rules obey the forms # ''A'' → ''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pushdown 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are 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). A formal grammar is "context-free" if 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. This is what distinguishes it from a context-sensitive grammar. 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, :\langle\text\rangle \to \langle\text\rangle = \langle\text\rangle ; replaces \langle\text\rangle with \langle\text\rangle = \langle\text\rangle ;. There can be multiple replacement rules for a given nonterminal symbol. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Bounded Automaton
In computer science, a linear bounded automaton (plural linear bounded automata, abbreviated LBA) is a restricted form of Turing machine. Operation A linear bounded automaton is a nondeterministic Turing machine that satisfies the following three conditions: * Its input alphabet includes two special symbols, serving as left and right endmarkers. * Its transitions may not print other symbols over the endmarkers. * Its transitions may neither move to the left of the left endmarker nor to the right of the right endmarker. In other words: instead of having potentially infinite tape on which to compute, computation is restricted to the portion of the tape containing the input plus the two tape squares holding the endmarkers. An alternative, less restrictive definition is as follows: * Like a Turing machine, an LBA possesses a tape made up of cells that can contain symbols from a finite alphabet, a head that can read from or write to one cell on the tape at a time and can be moved, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-sensitive Language
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the four types of grammars in the Chomsky hierarchy. Computational properties Computationally, a context-sensitive language is equivalent to a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(''O''(''n'')), because they can be accepted using linear space on a non-deterministic Turing machine. The class LINSPACE (or DSPACE(''O''(''n''))) is defined the same, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 equiva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write and which direction to move is based on a finite table that specifies what to do for each com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
