February 2013 (Spring drive)

Bachelor of Computer Application (BCA) – Semester 5

BC0052 – Theory of computer science – 4 Credits

(Book ID: B0972)

(60 Marks)

Answer the following questions. [10 6 = 60 Marks]

1. Using the definition of order show that 122 xx is )( 2xO .

2. Prove by mathematical induction

6

)12)(1(.......321 2222

nnn

n

3. Prove that “The sum of the degrees of the vertices of a graph G is twice the number of edges” 4. Prove that “A tree G with n vertices has (n–1) edges”

5. Draw the state diagram for the finite automation M = (Q, , q0, , F) where

= {a, b}, Q = {q0, q1, q2}, F = {q0, q1}, : Q Q defined by

6. Obtain a regular expression such that }1,0{/{)( wwRL } with atleast three

consecutive 0’s.

a b

q0 q0 q1 q1 q0 q2 q2 q2 q2