Such string operations are used to investigate closure properties of classes of languages. A class of languages is closed under a particular operation when the operation, applied to languages in the class, always produces a language in the same class again. For instance, the context-free languages are known to be closed under union, concatenation, and intersection with regular languages, but not closed under intersection or complement. The theory of trios and abstract families of languages studies the most common closure properties of language families in their own right., Chapter 11: Closure properties of families of languages.
such string operations are used to investigate closure properties of classes of languages a class of languages is closed under a particular operation when the operation applied to languages in the class always produces a language in the same class again for instance the context-free languages are known to be closed under union concatenation and intersection with regular languages but not closed under intersection or complement the theory of trios and abstract families of languages studies the most common closure properties of language families in their own right chapter 11 closure properties of families of languages