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Given a Deterministic Finite Automata (DFA), try to reduce the DFA by removing unreachable states and removing similar rows.

Remove the unreachable states from q0

From the initial states, we are not able to reach q2 and q4. So, remove these two states as shown below −

After removing unreachable states, the partial minimized DFA is as follows −

The **transition table** is given below −

States | 0 | 1 |
---|---|---|

->q0 | q1 | q3 |

q1 | q0 | q3 |

*q3 | q5 | q5 |

*q5 | q5 | q5 |

Divide tables into 2 tables as shown below −

**Table 1** starts from the non-final states.

States | 0 | 1 |
---|---|---|

->q0 | q1 | q3 |

q1 | q0 | q3 |

**Table 2** starts from the final states.

States | 0 | 1 |
---|---|---|

*q3 | q5 | q5 |

*q5 | q5 | q5 |

Remove similar rows.

Table 1 has no similar rows

Table 2 has similar rows. So, skip q5 and replace q5 by q3

States | 0 | 1 |
---|---|---|

q3 | q5 | q3 |

Combine two tables as shown below −

States | 0 | 1 |
---|---|---|

->q0 | q1 | q3 |

q1 | q0 | q3 |

*q3 | q3 | q3 |

Thus, the **minimized DFA** will be as follows −

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