This document discusses the steps to construct the transition table for an NFA with epsilon transitions. It begins by taking the epsilon closure of each state. It then determines the output states for each input symbol applied to each state/closure set by taking the epsilon closure. This information is used to construct the transition table and diagram. The transition table shows the output state(s) for each input applied to each state. The transition diagram visually depicts the transitions.

1. KANIMOZHI S
BE(CSE)

2. q1q0
q2
FS
a
b

5. Step1:
want to take a epsilon closure for all states
because it contains empty states
Step2:
Then check the inputs with all states .while
checking the with the input it will produce new
some states
Step3:
Then construct a transition table for the
respective outputs.

6. Step1:
Epsilon closure of q0={q0}
Because it not move to next state with epsilon
closure
For taking epsilon closure it contains the current
state then new state
Epsilon closure of q1={q1,q2}
Here it contains two state because the q1 is move
to next state with epsilon closure.
Epsilon closure of q2={q2}

7. Epsilon closure (q0)={q0}
Epsilon closure(q1)={q1,q2}
Epsilon closure(q2)={q2}

8. ’(q0,a)=epsilon closure( (q0,a))
=e-closure( (q0,epsilon),a)
=e-closure(e-closure(q0),a)[here e-closure of q0 is
only q0 so we can take e-closure of q0 is q0 alone]
=e-closure(q0,a)
=e-closure(q1) [finally the state q1 contains two
states q1,q2 as e-closure so we can take it]
={q1,q2}
’(q0,b)=epsilon closure( (q0,b))
=e-closure( (q0,epsilon),b)
=e-closure(e-closure(q0),b)[here e-closure of q0 is
only q0 so we can take e-closure of q0 is q0 alone]
=e-closure(q0,b)[here no input for q0,b so simply
write it as ]
=e-closure( )[no e-closure for so no states]
={ }

9. ’(q1,a)=epsilon closure( (q1,a))
=e-closure( (q1,epsilon),a)
=e-closure(e-closure(q1),a)[here e-closure of q1 is q1,q2 so we
can take e-closure of q1 is q1,q2]
= e-closure( (q1,q2),a)
= e-closure((q1,a)U(q2,a))
=e-closure( U ) [finally from the two states there is no input so
that is empty]
={ }
’(q1,b)=epsilon closure( (q1,b))
=e-closure( (q1,epsilon),b)
=e-closure(e-closure(q1,q2),b)[here e-closure of q1 is q1,q2 so we
can take e-closure of q1 is q1q2 alone]
=e-closure(q1,b)U(q2,b)[here for input (q1,b)is (q2,b) is q2 so
simply write as ( Uq2]
=e-closure(q2)[ e-closure for q2 is q2]
={q2}

10. ’(q2,a)=epsilon closure( (q2,a))
=e-closure( (q2,epsilon),a)
=e-closure(e-closure(q2),a)[here e-closure of q2 is q2
alone so take q2 only]
= e-closure( (q2),a)
= e-closure( )
=e-closure( ) [finally from the state there is no input
so that is empty]
={ }
’(q2,b)=epsilon closure( (q2,b))
=e-closure( (q2,epsilon),b)
=e-closure(e-closure(q2),b)[here e-closure of q2 is q2 so
we can take e-closure of q2 is q2 alone]
=e-closure(q2,b)[here for input (q2,b)is q2 so simply
write as (q2)]
=e-closure(q2)[ e-closure for q2 is q2]
={q2}

11. TRANSITION TABLE
a b
q0 (q1,q2)
q1
q2 q2

12. In the table the row it will denotes about
the states
The column it will denotes about the input
By the input checking process we can
construct the table

13. TRANSITION DIAGRAM
b
a b
q0 q1 q2
a

14. We can construct a transition
diagram using the transition table