GENERATORS OF CONES AND CYLINDERS

Publisher Summary This chapter presents some results and questions about algebraic languages. The study of this particular family can be justified by two main reasons. The first one is that these languages have a lot of applications because they involve the fundamental mechanism of recursion as a finite description for infinite objects. The second major reason is that this family has a lot of mathematical properties. The work on algebraic languages has three main goals: to know as much as possible on the structure of algebraic languages; to know about the structure of the family of algebraic languages; and to relate the structure of a language and the structure of the rational cone it generates. From a language theoretician's point of view, studying these notions is only a step toward the applications of the study of the structure of families of languages. The operations on languages have been considered since the beginning of the theory of languages. The most obvious operations are union, morphism, and inverse morphism.

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