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Generalizing the idea of self-similar groups defined by Mealy automata, weitroduce the notion of a self-similar automaton and a self-similar group over achanging alphabet. We show that every finitely generated residually-finitegroup is self-similar over an arbitrary unbounded changing alphabet. Weconstruct some naturally defined self-similar automaton representations over anunbounded changing alphabet for any lamplighter group $K\wr \mathbb{Z}$ with anarbitrary finitely generated (finite or infinite) abelian group $K$.

The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata