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# Epsilon NFA  (∈-NFA)

Epsilon NFA (∈
-NFA) is similar to the NFA but have just a minor difference which is epsilon (∈) move. The transitions without consuming an input symbol are called ∈-transitions.

• In the state diagrams, they are usually labeled with the Greek letter ∈ also called lamda.
• ∈-transitions provide a convenient way of modeling the systems
• Due to empty move, the first string of language may be a empty or epsilon.

Note: ∈ab∈a = aba, where ∈ is empty.

## Formal Definition of Epsilon-NFA

The formal definition of  ∈-NFA is represented through 5-tuple (Q, ∑, δ, q0, F) where,

• Q is a finite set of all states (q0, q1, q2,   … qn) where n is finite number
• is a finite set of symbols called the alphabet. i.e. {0, 1},
• δ : Q x (∑ U ∈) → 2Q is a total function called as transition function
• q0 is the initial state from where any input is processed (q0 ∈ Q).
• F is a set of final state/states where F will be subset ( ⊆ ) of Q.

## Examples of Epsilon-NFA

There are various examples of epsilon-NFA. let explain some of them.

### Example 01

Draw a Finite Automata which accept the string “ab”. ### Example 02

Draw a Finite Automata which accept the string “a or b”. ### Example 03

Draw a Finite Automata which can accept the string “a or b or c”. ### Example 04

Draw a Finite Automata which accept the string “a*” ### Example 05

Create a ∈-NFA for regular expression: (b)*a Help Other’s By Sharing…