**ε** stand to epsilon or null value in NFA. **ε**-closures of state q_{i} is the set of states including q_{i} where q_{i} can reach by any number of **ε** – moves of the given NFA.

**ε**-closures of q_{i} :-

– **ε**-closures of a state q_{i}, includes q_{i}.

– Set of states reachable from q_{i} on **ε** – moves.

– Set of states reachable from existing states in **ε**-closures, using **ε**-move, and so on.

**ε**-closures of various states in above figure are given below:

**ε**-closures of q_{0} = {q_{0}, q_{1}, q_{2}, q_{4}, q_{7}}

There are **ε**-moves from q_{0} to q_{1} ,

q_{0} to q_{7} ,

q_{1} to q_{2} ,

q_{1} to q_{4} .

**ε**-closures of q_{1} = {q_{1}, q_{2}, q_{4}}

There is no **ε**-moves from q_{1} to q_{4} , q_{1} to q_{2} .

**ε**-closures of q_{2} = {q_{2}}

There are **ε**-moves from q_{3} to q_{6} ,

q_{6} to q_{7} ,

q_{6} to q_{1} ,

q_{1} to q_{2} ,

q_{1} to q_{4}.

**ε**-closures of q_{4} = {q_{4}}

There is no **ε**-move from q_{4} .

**ε**-closures of q_{5} = {q_{5}, q_{6}, q_{7}, q_{1}, q_{2}, q_{4}}

There are **ε**-moves from q_{5} to q_{6} ,

q_{6} to q_{7} ,

q_{6} to q_{1} ,

q_{1} to q_{2} ,

q_{1} to q_{4}.

**ε**-closures of q_{6} = {q_{7}, q_{1}, q_{2}, q_{4}}

There are **ε**-moves from q_{6} to q_{7} ,

q_{6} to q_{1} ,

q_{1} to q_{2} ,

q_{1} to q_{4}.

**ε**-closures of q_{7} = {q_{7}}

There is no **ε**-moves from q_{7} .

**ε**-closures of various states are summarized below :

State | ε-closures |
---|---|

q_{0} | {q_{0}, q_{1}, q_{2}, q_{4}, q_{7}} |

q_{1} | {q_{1}, q_{2}, q_{4}} |

q_{2} | {q_{2}} |

q_{3} | {q_{3}, q_{6}, q_{7}, q_{1}, q_{2} ,q_{4}} |

q_{4} | {q_{4}} |

q_{5} | {q_{5}, q_{6}, q_{7}, q_{1}, q_{2} ,q_{4}} |

q_{6} | {q_{7}, q_{1}, q_{2} ,q_{4}} |

q_{7} | {q_{7}} |

**Recommended:**

- Introduction to Finite Automata
- Deterministic Finite Automata (DFA)
- Number of 1’s is a multiple of 3 on {0,1} using DFA
- Number of 1’s is not multiple of 3 on {0,1} using DFA
- DFA for Number of 1’s is even/odd and number of 0’s is even/odd
- DFA for number of 0’s divisible by five and 1’s divisible by 3
- DFA for All string of length at most five
- DFA for All strings ending with abb
- DFA for strings in which leftmost symbol differ from rightmost
- Design DFA that contain word ‘CAT’ using word ‘CHARIOT’
- Design DFA which accept a binary number divisible by 3
- Non-Deterministic finite Automata
- Design NFA to accept string containing the substring 0101
- Design NFA that accepts string ending with aab
- Differentiate between NFA and DFA
- Design NFA that start with 01 and end with 10