T-STRUCTURES, T-FUNCTIONS, AND TEXTS

The theory of 2-structures [see, e.g.. Ehrenfeucht and Rozenberg (1990)] provides a convenient framework for investigating various mathematical structures encountered in computer science. This paper investigates a subclass of 2-structures, called T-structures, which turned out to be important in the investigation of basic properties of 2-structures [see Ehrenfeucht and Rozenberg (1992)]. We prove that T-structures are a natural generalization of linear orders; in particular, we prove that a T-structure can be represented by two linear orders. Based on this result, the notion of a text is introduced which generalizes the notion of a word as used in formal language theory. A text may be seen as a word with a ''structure'' spanned on it; this structure may be a tree, but it may also be more general than a tree. Basic properties of the class of texts corresponding to trees are investigated.