1) An epsilon-NFA (ε-NFA) allows instantaneous transitions between states without reading an input symbol, represented by epsilon (ε) labels on arcs. 2) An ε-NFA is formally defined as a 5-tuple (Q, Σ, δ, q0, F) where Q is states, Σ is the alphabet, δ is the transition function, q0 is the initial state, and F are final states. Epsilon is not a member of the alphabet. 3) The epsilon-closure of a state p is the set of all states reachable from p through epsilon transitions.

1. Finite
Automaton
with ε - Moves
-Sampath Kumar S,
AP/CSE, SECE

2. Finite Automaton with ε - Moves
We extend the class of NFAs by allowing
instantaneous (ε) transitions:
1. The automaton may be allowed to change its state
without reading the input symbol.
2. In diagrams, such transitions are depicted by
labeling the appropriate arcs with ε.
3. Note that this does not mean that ε has become an
input symbol. On the contrary, we assume that the
symbol ε does not belong to any alphabet
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Sampath Kumar S, AP/CSE, SECE

3. Formal definition of ε-NFA:
A NFA can be represented by a 5-tuples (Q, ∑, δ,
q0, F) where −
 Q is a finite set of states.
 ∑ is a finite set of symbols, called the alphabet of
the automaton.
 δ: Q × Σε → P(Q) is the transition function .
 q0 is the initial state from where any input is
processed (q0 ∈ Q).
 F is a set of final state/states of Q (F ⊆ Q).
Note: Note ε is never a member of Σ
11/21/20173
Sampath Kumar S, AP/CSE, SECE

4. ε-Closure:
The ε-Closure is a set of all states which are
reachable from state p on ε-transitions such that:
1. ε-Closure (p) = p where p ∈ Q.
2. If there exist ε-Closure (p) ={q} and δ (q, ε) = r then
ε-Closure (p) = {q, r}
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Sampath Kumar S, AP/CSE, SECE

5. Example
20. Find the ε-Closure for the following NFA with ε.
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Sampath Kumar S, AP/CSE, SECE

6. Example
21. Find the ε-Closure for the following NFA with ε.
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Sampath Kumar S, AP/CSE, SECE

7. 11/21/2017
Sampath Kumar S, AP/CSE, SECE
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8. நன்றி
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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