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July 2011
Master of Computer Application (MCA) Semester 5
MC0082 Theory of Computer Science 4 Credits
(Book ID: B0970)
Assignment Set 1 (60 Marks)
Answer the following : 610 = 6
1. Prove by the method of mathematical induction that
4
)1(...21
22333
nn
n
10 marks
2. Construct a grammer for the language
L = { x/x{a, b}, the number of as in xis a multiple of 3}
10 marks
3. Prove that the sum of the degrees of the vertices of a graph
G is twice the number of edges
10 marks
4. Obtain a DFA to accept strings of as and bs starting with the
string ab.
10 marks
5. Write briefly about the concept of Deterministic Finite
Automata (DFA)
10 marks
6. Convert the Moore machine M1 whose state table is given in
table below into an equivalent
Mealy machine
Moore Machine
Present State Next state Output
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Input a = 0 Input a =1
q0 q1 q2 1
q1 q3 q2 0
q2 q2 q1 1
q3 q0 q3 1
10 marks
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July 2011
Master of Computer Application (MCA) Semester 5
MC0082 Theory of Computer Science 4 Credits
(Book ID: B0970)
Assignment Set 2 (60 Marks)
Answer the following : 610 = 6
1. Construct a DFA and the transition diagram , to accept the
language generated by the
following grammar
S 01A
A 10B
B 0A11
10 marks
2. Prove the theorem
If L1 and L2 are regular, then the regular language is closed
under intersection.
10 marks
3. Construct a grammer for the language
L = {aaaa, aabb, bbaa, bbbb}
10 marks
4. Obtain a PDA to accept the language L = {anbn/ n 1} by a
final state
10 marks
5. State and prove pumping lemma for Context Free Languages
10 marks
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6. Find a Turing machine to accept the language containing
strings of 0s and 1s ending with
011 10 marks
