Abstract
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 F s T 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. F s T 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.
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