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# Generate a Regular Expression for a Finite Automata with state elimination method

## Problem

Given a Finite Automata, we need to convert the Finite Automata into equivalent Regular Expression using the State Elimination Method.

**Step 1** − Initial state q1 has incoming edge. So, create a new initial state qi.

**Step 2** − Final state q2 has outgoing edge. So, create a new final state.

**Step 3** − Start eliminating intermediate states one after another.

- If there is path going to qi to q2 via q1
- So after eliminating q1 we can connect a direct path from qi to q2 having cost
ε .c*.a=c*a

- There is a loop on q2 using state qi
- So after eliminating state q1 we can draw a direct loop on state q2 having cost
b.c*.a=b.c*.a

**Step 4**

Now eliminate q2.

After eliminating q2 direct path from state qi to qf having cost.

c*a(d+bc*a) * ε=c*a(d+bc*a)*

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