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Productions (computer Science)
A production or production rule in computer science is a ''rewrite rule'' specifying a symbol substitution that can be recursively performed to generate new symbol sequences. 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 leave 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 st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rewrite Rule
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 ... [...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. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grammar
In linguistics, the grammar of a natural language is its set of structure, structural constraints on speakers' or writers' composition of clause (linguistics), clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes domains such as phonology, morphology (linguistics), morphology, and syntax, often complemented by phonetics, semantics, and pragmatics. There are currently two different approaches to the study of grammar: traditional grammar and Grammar#Theoretical frameworks, theoretical grammar. Fluency, Fluent speakers of a variety (linguistics), language variety or ''lect'' have effectively internalized these constraints, the vast majority of which – at least in the case of one's First language, native language(s) – are language acquisition, acquired not by conscious study or language teaching, instruction but by hearing other speakers. Much of this internalization occurs during early childhood; learning a language later ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post Canonical System
A Post canonical system, also known as a Post production system, as created by Emil Post, is a string-manipulation system that starts with finitely-many strings and repeatedly transforms them by applying a finite set j of specified rules of a certain form, thus generating a formal language. Today they are mainly of historical relevance because every Post canonical system can be reduced to a string rewriting system (semi-Thue system), which is a simpler formulation. Both formalisms are Turing complete. Definition A Post canonical system is a triplet (A,I,R), where * A is a finite alphabet, and finite (possibly empty) strings on A are called ''words''. * I is a finite set of ''initial words''. * R is a finite set of string-transforming rules (called '' production rules''), each rule being of the following form: : \overset where each and is a specified fixed word, and each ''$'' and ''$' '' is a variable standing for an arbitrary word. The strings before and after the arrow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
