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# Construct ∈-NFA of Regular Language L = (00)*1(11)*

The ε transitions in Non-deterministic finite automata (NFA) are used to move from one state to another without having any symbol from the 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 also has five states same as DFA, but with different transition function, as shown follows −

$$\delta\colon\:Q\times\:\sum\longrightarrow\:2^{Q}$$

Where,

Q: Finite set of states

Σ: Finite set of the input symbol

- q0: Initial state
F: Final state

δ: Transition function

Let’s consider the given language L = (00)*1(11)*.

The given language is divided into three parts (00)*, 1 and (11)*. Let’s construct the transition diagram for each part and finally concatenate the three parts to get the final result.

**Step 1** − NFA with epsilon for (00)* is as follows −

**Step 2** − NFA with epsilon for (11)* is as follows −

**Step 3** − Concatenate first and second part with 1 in between, as follows −

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