Forest Categories

A growing body of research into the expressive power of logics on trees has employed algebraic methods—especially the syntactic forest algebra, a generalization of the syntactic monoid of regular languages. Here we enlarge the mathematical foundations of this study by extending Tilson’s theory of the algebra of finite categories, and in particular, the Derived Category Theorem, to the setting of forest algebras. As an illustration of the usefulness of these methods, we provide a new treatment of the recent results of Place and Segoufin on locally testable tree languages.