# 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, q_{0}, F) where,

**Q**is a finite set of all states (q_{0, }q_{1, }q_{2, … }q_{n}) where n is finite number**∑**is a finite set of symbols called the alphabet. i.e. {0, 1},**δ : Q x (∑ U ∈) → 2**^{Q}is a total function called as transition function**q**is the initial state from where any input is processed (q_{0 }_{0}∈ 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**