NFA with ∈ to DFA Indirect Method

Indirect Method: In this method,

Step 01: Convert NFA with ∈ moves to NFA without ∈ moves.

Step 02: Than NFA without ∈ moves is converted to the DFA.

For example: Convert he following NFA with ε in to DFA using Indirect method of comversion ?

NFA with ∈

Solution: Step 01: Convert NFA with ∈ moves to NFA without

∈ moves.∈-Closure of q0: {q0, q1, q2}

∈-Closure of q1: {q1, q2}

∈-Closure of q2: {q2}

StateabC
è q0{q0, q1, q2}{q1, q2}{q2}
q1Φ{q1, q2}{q2}
q2ΦΦ{q2}

NFA without ∈ Transition table
Step 02: NFA without ∈ moves is converted to the DFA using Subset construction method.

StateabC
{q0}{q0, q1, q2}{q1, q2}{q2}
{q1}DeadState{q1, q2}{q2}
{q2}DeadStateDeadState{q2}
{q0, q1, q2}{q0, q1, q2}{q1, q2}{q2}
{q1, q2}DeadState{q1, q2}{q2}
DeadStateDeadStateDeadStateDeadState