TOC-grand test-Q11

Question

Consider the computational problems about the context free languages given below.

P1 : on input a PDA, determine if the height of its stack exceeds 2019 in any computation.

P2 : on input a context-free grammar, determine if it generates infinitely many strings in

P3 : on input a PDA P; determine if P can ever enter an accept state with its stack empty;

P4 : on input a context-free grammar G; determine if L(G) is finite.

Which of the above problems are UNDECIDABLE ?

(A) Only P4

(B) P2 and P3

(C) P1 and P4

(D) None of them

Answer 1

P1 : DECIDABLE

 

Let P be a given PDA. Modify P to keep track of the maximum stack height so far, the possibilities being 0,1,..,2019,2019+. This added functionality can be implemented as part of the state. Modify the automaton further to accept its input iff the maximum stack height so far is 2019+. Finally, use the algorithm from class to check whether the resulting PDA accepts any strings.

 

P2 : DECIDABLE

 

 

P3 : DECIDABLE

 

 

P4 : DECIDABLE

 

Hence Option D

Answer 2

ANS D

P4-  Finiteness prob of cfl is Decidable. 

P3- Decidable, Membership prob. 

P1- Decidable .

P2- Decidable