Abstract: Automata theory is an important component of computer science. This paper considers the linear autonomous automata over finite Boolean algebra. In fact, any finite automaton over finite Field can be regarded as a Boolean function-matrix automaton. It presents a reversible linear autonomous automaton over finite Boolean algebra. A necessary and sufficient condition is given and proved for an automaton to be a forest. Thirdly, a formula counting the nodes of tree is put forward. Finally, A necessary and sufficient condition is given and proved for an autonomous automaton to be a equal-branch-tree.