This paper proposes a method for obtaining a minimal LTLf
automaton. The method is based on Brzozowski's theory of minimal automata construction, completing the construction of a minimal DFA from LTLf. The method includes: for a given LTLf formula, first using the tool MONA to construct a corresponding inverse deterministic
automaton for the LTLf, which can accept reverse sequences of the original LTLf receiving language; inverting the inverse deterministic
automaton to obtain a nondeterministic
finite state automaton (NFA); performing a subset construction calculation on the NFA, and then performing a reachable state calculation to remove all unreachable states. According to Brzozowski's theory, this DFA is the minimized DFA corresponding to the LTLf formula.