DFA to Regular Expression Multiple Final States

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In this class, We discuss DFA to Regular Expression Multiple Final States.

The reader should have a prior understanding of DFA to Regular Expression using the ardens method. Click Here.

The below diagram is our example DFA with multiple final states.

First, we write equations for each state.

A = A0 + ε

B = A1 + B1

C = B0 + C(0 + 1)

Take the first equation

A = A0 + ε

The above equation is of the form R = Q + RP

R = A

Q = ε

P = 0

We can write R = QP*

A = 0*

Substitute A in B

B = A1 + B1

B= 0*1 + B1

The above equation is of the form R = Q + RP

B = 0*11*

The final regular expression is 0* + 0*11*

State A union state B is considered the final regular expression because A and B are final states.