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


Answer: (A)

Explanation:

• 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.

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