Monadic second-order definable text languages

Atext is a word together with a (additional) linear ordering. Each text has a generic tree representation, called itsshape. Texts are considered in a logical and in an algebraic framework. It is proved that, for texts of bounded primitivity, the class of monadic second-order definable text languages coincides with both the class of recognizable text languages and the class of text languages generated by right-linear text grammars. In particular it is demonstrated that the construction of the shape of a text can be formalized in terms of our monadic second-order logic. This approach can be extended to the case of graphs.

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