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Ayesha Kanwal

Every finite automaton has an equivalent regular expression.

The conversion of a finite automaton to a regular expression is done through the **state elimination method**.

The State elimination method follows the following general set of rules:

- Add a new initial state (
$I$ ). Make a null transition from the old initial state to the new initial state. - Add a new final state (
$F$ ). Make null transition(s) to the new final state. - Eliminate all states, except
$I$ and$F$ , in the given finite automaton. Perform the elimination of states by checking the andin-degrees A transition into a state of states and taking a cross product.out-degrees A transition moving away from a state

After steps 1 and 2, the

Let's consider the following finite automaton:

Add a new initial state,

Add a new final state,

Perform the elimination of states other than

Eliminate state

Eliminate state _{. }Concatenate transitions from state

Eliminate

Eliminate state

Put it all together.

The resultant regular expression for the given finite automaton is as follows:

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