Designing a DFA and the reverse of it
$L^R$ is the reverse of the language $L$ and for designing $L^R$ you must:


Reverse all edges in the transition diagram.
The accepting state for the LR automaton is the start state for the main automaton.
Create a new start state for the new automaton with epsilon transitions to reach of the accept states for the main automaton.
Convert this NFA back into a DFA.