NAME : VIKASH KUMAR

ROLL NUMBER : 511037846

LEARNING CENTER : INSOFT

LEARNING CENTER CODE 01822, Noida

COURSE : MCA

SEMESTER : 5TH

SUBJECT : Theory of Computer Science

MODULE NO. (Set No.) : 1

DATE OF SUBMISSION :

FACULTY SIGNATURE :

Directorate of Distance EducationSikkim Manipal University2nd Floor, Syndicate House

Manipal-576104

1

Master of Computer Application (MCA) – Semester 5MC0082 – Theory of Computer Science

Assignment Set – 1

Que1. Prove by the principle of mathematical induction that

Base Step:

Let n=0 then the sum of the left side is 0

Since there is nothing to add the expression on the right side is also 0

If n=1 then left side is 1

& right side =

Hence the result is true for n=1

Induction Hypothesis:

Assume that the result to be true for n=m then

Adding the (m+1)th term i.e (m+1)3 to both side of the above equation

2

There for the result is true for n=m+1. Hence the mathematical induction, the given result

is true for all positive integer n.

Que2: The number of vertices of odd degrees is always even.

Ans2.

Que 3. Construct a grammer for the language L = {x/x {a, b}, the number of a’s in x is a multiple of 3}

Ans:-

3

Q.4. Briefly explain in your own words “Turing machine model”.

A.4. Turing Machine Model

4

Que.5. Define a Pushdown automata and explain its construction.

Ans. 5.

5

Q.6. Explain “Backus-Naur Form”.

6

A.6.

7

NAME : VIKASH KUMAR

ROLL NUMBER : 511037846

LEARNING CENTER : INSOFT

LEARNING CENTER CODE 01822, Noida

COURSE : MCA

SEMESTER : 5TH

SUBJECT : Theory of Computer Science

MODULE NO. (Set No.) : 2

DATE OF SUBMISSION :

FACULTY SIGNATURE :

Directorate of Distance EducationSikkim Manipal University2nd Floor, Syndicate House

Manipal-576104

8

Master of Computer Application (MCA) – Semester 5MC0082 – Theory of Computer Science

Assignment Set – 2

Q.1. Prove that any connected graph with n vertices and n-1 edges is a tree.

A.1.

Q.2. Construct a grammar for the language

L={aaaa, aabb, bbaa, bbbb}.

9

A.2.

Q.3. Briefly write in your own words the concept of transition graph.

A.3.

10

Q.4.Explain the steps involved in the conversion of mealy machine into moore machine.

A.4.

11

Q.5. Differentiate between DFA and NDFA.

A.5.

12