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Equivalence (formal Languages)
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees are reasonably similar in that the same semantic interpretation can be assigned to both. Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages. On the other hand, if two grammars generate the same set of derivation trees (or more generally, the same set of abstract syntactic objects), then the two grammars are strongly equivalent. Chomsky (1963) introduces the notion of strong equivalence, and argues that only strong equivalence is relevant when comparing grammar formalisms. Kornai and Pullum (1990)Kornai, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called ''well-formed words''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. 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 meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In ... [...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] |
Generative Grammar
Generative grammar is a research tradition in linguistics that aims to explain the cognitive basis of language by formulating and testing explicit models of humans' subconscious grammatical knowledge. Generative linguists, or generativists (), tend to share certain working assumptions such as the competence–performance distinction and the notion that some domain-specific aspects of grammar are partly innate in humans. These assumptions are rejected in non-generative approaches such as usage-based models of language. Generative linguistics includes work in core areas such as syntax, semantics, phonology, psycholinguistics, and language acquisition, with additional extensions to topics including biolinguistics and music cognition. Generative grammar began in the late 1950s with the work of Noam Chomsky, having roots in earlier approaches such as structural linguistics. The earliest version of Chomsky's model was called Transformational grammar, with subsequent itera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postfix Traversal
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well. Types Unlike linked lists, one-dimensional arrays and other linear data structures, which are canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in depth-first or breadth-first order. There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex or hybrid schemes are possible, such as depth-limited searches like iterative deepening depth-first search. The latter, as well as breadth-first search, can also be used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Operations
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a ''higher'' precedence is performed before operations with ''lower'' precedence. Calculators generally perform operations with the same precedence from left to right, but some programming languages and calculators adopt different conventions. For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern mathematical notation, algebraic notation. Thus, in the expression , the multiplication is performed before addition, and the expression has the value , and not . When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concrete Syntax Tree
A parse tree or parsing tree (also known as a derivation tree or concrete syntax tree) is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar. The term ''parse tree'' itself is used primarily in computational linguistics; in theoretical syntax, the term ''syntax tree'' is more common. Concrete syntax trees reflect the syntax of the input language, making them distinct from the abstract syntax trees used in computer programming. Unlike Reed-Kellogg sentence diagrams used for teaching grammar, parse trees do not use distinct symbol shapes for different types of constituents. Parse trees are usually constructed based on either the constituency relation of constituency grammars (phrase structure grammars) or the dependency relation of dependency grammars. Parse trees may be generated for sentences in natural languages (see natural language processing), as well as during processing of computer languages, such as progra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Start Symbol (formal Languages)
A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the 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, 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 determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parse Tree Derivations ETF
Parsing, syntax analysis, or syntactic analysis is a process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar by breaking it into parts. The term ''parsing'' comes from Latin ''pars'' (''orationis''), meaning part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams. It usually emphasizes the importance of grammatical divisions such as subject and predicate. Within computational linguistics the term is used to refer to the formal analysis by a computer of a sentence or other string of words into its constituents, resulting in a parse tree showing their syntactic relation to each other, which may also contain semantic information. Some parsing algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammars
A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the 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, 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 determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Head-driven Phrase Structure Grammar
Head-driven phrase structure grammar (HPSG) is a highly lexicalized, constraint-based grammar developed by Carl Pollard and Ivan Sag. It is a type of phrase structure grammar, as opposed to a dependency grammar, and it is the immediate successor to generalized phrase structure grammar. HPSG draws from other fields such as computer science (type system, data type theory and knowledge representation) and uses Ferdinand de Saussure's notion of the sign (linguistics), sign. It uses a uniform formalism and is organized in a modular way which makes it attractive for natural language processing. An HPSG includes principles and grammar rules and lexicon entries which are normally not considered to belong to a grammar. The formalism is based on lexicalism. This means that the lexicon is more than just a list of entries; it is in itself richly structured. Individual entries are marked with types. Types form a hierarchy. Early versions of the grammar were very lexicalized with few grammatica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
