GATE-CS-2003

Question 11

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

• Θ(1)
• Θ(log n)
• Θ(n)
• Θ(n²)

Question 12

Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions ?

• Π is NP-hard but not NP-complete
• Π is in NP, but is not NP-complete
• Π is NP-complete
• Π is neither NP-hard, nor in NP

Question 13

Nobody knows yet if P = NP. Consider the language L defined as follows : Which of the following statements is true ?

• L is recursive
• L is recursively enumerable but not recursive
• L is not recursively enumerable
• Whether L is recursive or not will be known after we find out if P = NP

Question 14

The regular expression 0*(10*)* denotes the same set as

• (1*0)*1*
• 0 + (0 + 10)*
• (0 + 1)* 10(0 + 1)*
• none of these

Question 15

If the strings of a language L can be effectively enumerated in lexicographic (i.e., alphabetic) order, which of the following statements is true ?

• L is necessarily finite
• L is regular but not necessarily finite
• L is context free but not necessarily regular
• L is recursive but not necessarily context free

Question 16

Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?

• Removing left recursion alone
• Factoring the grammar alone
• Removing left recursion and factoring the grammar
• None of these

Question 17

Assume that the SLR parser for a grammar G has n1 states and the LALR parser for G has n2 states. The relationship between n1 and n2 is:

• n1 is necessarily less than n2
• n1 is necessarily equal to n2
• n1 is necessarily greater than n2
• none of these

Question 18

In a bottom-up evaluation of a syntax directed definition, inherited attributes can

• always be evaluated
• be evaluated only if the definition is L-­attributed
• be evaluated only if the definition has synthesized attributes
• never be evaluated

Question 19

Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree ?

• 7 5 1 0 3 2 4 6 8 9
• 0 2 4 3 1 6 5 9 8 7
• 0 1 2 3 4 5 6 7 8 9
• 9 8 6 4 2 3 0 1 5 7

Question 20

Consider the following three claims

1. (n + k)m = Θ(nm), where k and m are constants
2. 2n + 1 = O(2n)
3. 22n + 1 = O(2n) 

Which of these claims are correct ?

• 1 and 2
• 1 and 3
• 2 and 3
• 1, 2, and 3