formal languages and automata theory

formal language is a set of strings of symbols drawn from a finite alphabet. A formal language can be specified either by a set of rules (such as regular expressions or a context-free grammar) that generates the language, or by a formal machine that accepts (recognizes) the language. A formal machine takes strings of symbols as input and outputs either “yes” or “no.” A machine is said to accept a language if it says “yes” to all and only those strings that are in the language. Alternatively, a language can be defined as the set of strings for which a particular machine says “yes.” Formal languages can be grouped into a series of successively larger classes known as the Chomsky hierarchy.14 Most of the classes can be characterized in two ways: by the types of rules that can be used to generate the set of strings, or by the type of formal machine that is capable of recognizing the language