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# Explain with an example how to convert NFA to DFA.

## Problem

Convert the following Non-Deterministic Finite Automata (NFA) to Deterministic Finite Automata (DFA).

## Solution

The transition diagram is as follows −

The transition table of NFA is as follows −

State | a | b |
---|---|---|

->q0 | q0 | q0,q1 |

q1 | - | *q2 |

*q2 | - | - |

The DFA table cannot have multiple states. So, make q0q1 as a single state.

Let’s convert the given NFA to DFA by considering two states as a single state.

The transition table of DFA is as follows −

State | a | b |
---|---|---|

->q0 | q0 | [q0,q1] |

[q0q1] | [q0] | [q0q1q2] |

*[q0q1q2] | [q0] | [q0q1q2] |

In the above transition table, q2 is the final state. Wherever, q2 is present that becomes the final state.

**Note** −

- After conversion the number of states in the final DFA may or may not be the same as in NFA.
- The maximum number of states present in DFA may be 2pow (number of states in NFA)
- The relationship between number of states in NFA and DFA is: 1<=n<=2m
Where n= number of states in DFA

m= number of states in NFA

- The final DFA all states that contain the final states of NFA are treated as final states.

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