  The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is
used to define and study automorphism groups of the tree $X^*$ of finite words
over $X$. The concept of bi-reversibility for Mealy-type automata is extended
to automata over a changing alphabet. It is proved that a non-abelian free
group can be generated by a two-state bi-reversible automaton over a changing
alphabet $X=(X_i)_{i\geq 1}$ if and only if $X$ is unbounded. The
characterization of groups generated by a two-state bi-reversible automaton
over the sequence of binary alphabets is established.
