AN ALGEBRAIC MODEL OF SYNCHRONOUS SYSTEMS

Finite state structural Mealy automata over an algebraic theory T (called structural T-automata) are introduced to model behaviors of synchronous systems. The main result is a left adjoint construction which extends the algebraic theory T to a strong feedback theory FsT by adjoining the operation of feedback to it. Structural T-automata equipped with simulations as vertical arrows between them form a symmetric monoidal 2-category. FsT is obtained by divesting this 2-category of its vertical structure, i.e., by making equivalent all the automata contained in the same connected component of a given hom-category. It is shown that, up to isomorphism of 2-cells, each equivalence class contains a unique automaton which is minimal regarding the number of its registers. © 1992.