**Steps to convert epsilon - NFA to NFA**

This section will cover the steps to convert epsilon - NFA to NFA.

Also read - __Arden's theorem__

Letâ€™s take an example of Q (a finite set of states) and understand the below-mentioned steps to convert epsilon - NFA to NFA by removing all the epsilon moves in it:

Given Q:

Figure 1

**Step 1: **Consider two states having epsilon moves between them. Take two vertices, â€˜srcâ€™ and â€˜dest,â€™ such that

src = Starting state of the epsilon move

dest = Destination state of the epsilon move

In Q, we can see an epsilon move from state q0 to q1 that needs to be removed, so consider them.

src = q_{0}

dest = q_{1}

Figure 2

**Step 2: **Find all the moves starting from â€˜destâ€™.

Here, dest = q_{1}

All the moves starting from q_{1} are:

Figure 3

**Step 3: **Remove the epsilon move and copy all the above-found moves starting from â€˜destâ€™ to start from â€˜srcâ€™ with the same input.

Here, src = q_{0} and dest = q_{1}

After removing the epsilon move and creating the copy of all the moves starting from q1 to start from q0 with the same input, Q will be converted to:

Figure 4

**Step 4: ** If state â€˜destâ€™ is a final state, then make the state â€˜srcâ€™ also a final state.

Here, dest = q_{1}

As q_{1} is a final state, q_{0} will also be converted to a final state

After converting q_{0} to a final state, Q will be converted to:

Figure 5

**Step 5: ** If state â€˜srcâ€™ is a start state, then make the state â€˜destâ€™ also a final state.

Here, src = q_{0}

As q_{0} is a start state, q_{1} will also be converted to a start state

After converting q_{1} to a start state, Q will be converted to:

Figure 6

**Step 6: ** Repeat steps 1-4 for all the remaining epsilon moves. If there is no epsilon move left, then stop.

Here we can see that there are no epsilon moves left. So, given Q shown in â€˜figure 1â€™ will be converted to â€˜figure 6â€™ after removing all the epsilon moves in the process of conversion of epsilon - NFA to NFA.

Also see, __Turing Machine in TOC____.__

**Frequently Asked Questions**

### What is epsilon in NFA?

In NFA (nondeterministic finite automata), the symbol "epsilon" (Îµ) refers to a transition that doesn't require any input or an empty string. Essentially, it allows an NFA to change from one state to another without consuming any input.

### What is epsilon closure of an NFA?

In NFA, the epsilon closure (Îµ-closure) is a set of states reachable from a specific state through epsilon transitions that don't consume any input. It includes the starting state and all states that can be reached via epsilon transitions from that state.

### How do you convert epsilon NFA to NFA?

To convert an epsilon NFA (Îµ-NFA) to an NFA, remove all epsilon transitions first. Create new transitions for every potential transition combination. Create a new transition table and set of accepted states for the converted NFA.

### What is epsilon in DFA?

Epsilon(Îµ) in DFA (deterministic finite automata) signifies a non-existent input symbol or a null transition. Epsilon transitions are not permitted in DFA, unlike in NFA (nondeterministic finite automata). As a result, epsilon transitions are inapplicable in DFA.

**Conclusion**

This article discussed the method of conversion of epsilon - NFA to NFA. We also briefly discussed what epsilon is in NFA and some frequently asked questions.

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