designing a DFA and the reverse of it

Problem Detail: 

There is a theorem that says if a language is regular, it's reverse is regular as well. How can I draw a DFA that shows if a language is regular, it's regular as well?

Asked By : Parisa

Answered By : Parisa

$L^R$ is the reverse of the language $L$ and for designing $L^R$ you must:

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

Hope this helps. Good luck

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Question Source : http://cs.stackexchange.com/questions/39622