![’(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]
={ }](https://image.slidesharecdn.com/newmicrosoftofficepowerpointpresentation-180322155513/85/simple-problem-to-convert-NFA-with-epsilon-to-without-epsilon-8-320.jpg)
![’(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}](https://image.slidesharecdn.com/newmicrosoftofficepowerpointpresentation-180322155513/85/simple-problem-to-convert-NFA-with-epsilon-to-without-epsilon-9-320.jpg)
![’(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}](https://image.slidesharecdn.com/newmicrosoftofficepowerpointpresentation-180322155513/85/simple-problem-to-convert-NFA-with-epsilon-to-without-epsilon-10-320.jpg)
simple problem to convert NFA with epsilon to without epsilon
- 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