GATE | GATE-CS-2000 | Question 32
Consider the following decision problems:
(P1) Does a given finite state machine accept a given string (P2) Does a given context free grammar generate an infinite number of stings
Which of the following statements is true?
(A) Both (P1) and (P2) are decidable
(B) Neither (P1) nor (P2) are decidable
(C) Only (P1) is decidable
(D) Only (P2) is decidable
- A finite state machine always halts in final or non-final state.Therefore, problem P1 is decidable.
- We check if the context free language generates any string of length between n and (2n – 1). If so, context free language is infinite else it is finite.Therefore, problem P2 is decidable.
Thus, option (A) is correct.
Please comment below if you find anything wrong in the above post.