Regular language to finite automaton

Question

I am trying to tun the following regular language into a finite automata, but I am confused by the U (union) and I am unsure of how to approach this part of the expression.

The expression: $$ L[01((0 \cup 11)11^*)^*0] $$

Answer 1

Union is easy: $$ (0 \cup 11) $$ means both $0$ and $11$ are recognized. This means there exist transitions from the state $q_i$ before the opening parenthesis to the state $q_j$ after the closing parenthesis, one via accepting $0$ and another one via accepting $11$: $$ \delta(q_i, 0) = q_j \\ \delta(q_i, 11) = q_j $$

                                             0
                                           ____
                                          /    v

                                      q_i        q_j

                                          \____^ 

                                            11