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 strings

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.

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