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There are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE). These methods are as follows −

- Arden's Theorem Method.
- State Elimination Method.

Now, let us learn about the state elimination method used in TOC.

- Initial state of DFA does not have any incoming edge.
- If there exists any incoming edge to the initial state, then we need to create a new initial state which has no incoming edge to it.

An example about the relation between incoming edge and initial state is given below−

- There must be only one final state in DFA.
- If there exist multiple final states in DFA, then we need to convert all final states into non-final states and create a new single final state.

An example of multiple final states and final states is as follows−

- The final state of DFA does not have any outgoing edge
- If there exists any outgoing edge from the final state, then we need to create a new final state which has no outgoing edge from it.

An example of outgoing edge and a new final state is given below −

- Eliminate all intermediate states one after the another. These states can be eliminated in any order.
- Finally, only an initial state which is going to the final state will be there
- The cost of this transition is the required Regular Expression.

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