Option 1- It is trivial that it is regular.
Option 2-
Case1- When number of b is greater or equal to number of a
In this case using only 51 state we can accept this. States will be like (# of b, #of a) which is(0,0) (1,0), (2,0), (3,0)………(50,0).
Case 2- When number of an is greater than number of b
In this case, we can not accept input string using finite state automata.
Because there is an infinite number of cases possible which should be accepted. (0,1), (0,2)………….(0,∞), (1,2), (1,3)…...∞) likewise. For all these, # of b – # of a is less than 50.
So option 2 is false.
