Theories, Pre-Theories and Finite State Transformations on Trees

Abstract

The closure of an algebra is defined as a generalization of the semigroup of a finite automation. Pretheories are defined as a subclass of the closed algebras, and the relationship between pretheories and the algebraic theories of Lawrence [1963] is explored. Finally, pretheories are applied to the characterization problem of finite state transformations on trees, solving an open problem of Thatcher [1969].