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Cone (formal Languages)
In formal language theory, a cone is a set of formal languages that has some desirable closure properties enjoyed by some well-known sets of languages, in particular by the families of regular languages, context-free languages and the recursively enumerable languages. The concept of a cone is a more abstract notion that subsumes all of these families. A similar notion is the faithful cone, having somewhat relaxed conditions. For example, the context-sensitive languages do not form a cone, but still have the required properties to form a faithful cone. The terminology ''cone'' has a French origin. In the American oriented literature one usually speaks of a ''full trio''. The ''trio'' corresponds to the faithful cone. Definition A cone is a family \mathcal of languages such that \mathcal contains at least one non-empty language, and for any L \in \mathcal over some alphabet \Sigma, * if h is a homomorphism from \Sigma^\ast to some \Delta^\ast, the language h(L) is in \mathcal; * if h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language Theory
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 complexity t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
