GATE | Gate IT 2005 | Question 37

Consider the non-deterministic finite automaton (NFA) shown in the figure.





State X is the starting state of the automaton. Let the language accepted by the NFA with Y as the only accepting state be L1. Similarly, let the language accepted by the NFA with Z as the only accepting state be L2. Which of the following statements about L1 and L2 is TRUE?

Correction in Question:
There is an edge from Z->Y labeled 0 and another edge from Y->Z labeled 1 – in place of double arrowed and no arrowed edges.

(A) L1 = L2
(B) L1 ⊂ L2
(C) L2 ⊂ L1
(D) None of the above


Answer: (A)

Explanation: According to Arden’s Theorem,



For y as final state:

Y = X0 + Y0 + Z1 

For z as final state:

Z = X0 + Y0 + Z1 

Hence,

L(Y) = L(Z) 

So, option (A) is correct.


Quiz of this Question



My Personal Notes arrow_drop_up


Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.