Elementary definability of the class of universal planar automata in the class of semigroups

Universal planar automata are universal attracting objects in the category of semigroup automata whose set of states and set of output signals are equipped with algebraic structures of the planes that are invariant under the actions of the transition and output functions. We establish the elementary definability of the class of universal planar automata in the class of semigroups and study the problem of the elementary classification of universal planar automata with the use of first-order theories of input signal semigroups of these automata.