Yes.
According to the automaton, a single dollar sign is a legal Java identifier. This is actually true, although it is a very poor choice for a variable name.
The automaton does not show the rules that a variable name cannot be a reserved word and that a variable name must be unique within its scope. Rules like these are defined by means other than finite automata. Here is a new automaton:
This automaton can stay in state q0 by consuming any sequence of a and b characters, or immediately go to the final state q1 by consuming a c, d, or e. Once in the final state, it can consume any number of f characters.
Which of the following strings are accepted by the new automaton?