State Elimination Method in Theory of Computation

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.

State Elimination Method

Step 1

• 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−

Step 2

• 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−

Step 3

• 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 −

Step 4

• 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.