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# Construct a ∈-NFA for the language L = (a* + b*)

The ε transitions in Non-deterministic finite automata (NFA) are used to move from one state to another without having any symbol from input set Σ

ε-NFA is defined in five-tuple representation

{Q, q0, Σ, δ, F}

Where,

δ − Q × (Σ∪ε)→2

^{Q}Q − Finite set of states

Σ − Finite set of the input symbol

q0 − Initial state

F − Final state

δ − Transition function

## NFA without ε transition

NFA is defined in five tuple representation

{Q, q0, Σ, δ, F}

Where,

δ − Q X Σ→ 2

^{Q}Q − Finite set of states

Σ − Finite set of the input symbol

q0 − Initial state

F − Final state

δ − Transition function

NFA and NFA with epsilon both are almost the same; the only difference is their transition function.

Let’s consider the given language L = (a*+b*)

## Steps for construction ε-NFA

**Step 1 **− NFA with epsilon for a* is as follows −

a^{*} means there can be any number of ‘a’ in the expression, even 0 ( if the input symbol is null then also it is valid).

**Step 2** − NFA with epsilon for b* is as follows −

b^{*} means there can be any number of b’s in the expression, even 0 (if input symbol is null then also it is valid).

**Step 3** − Now construct a*+b* using first and second steps.

The given language is divided into two parts like a* and b* and add two steps by using ‘+’ sign to get the result.

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