TOC Question Bank 2079 - With Solution

Tribhuvan University

Institute of Science and Technology

2079

Bachelor Level / fourth-semester / Science

Computer Science and Information Technology (CSC257)

Theory of Computation

Full Marks: 60 + 20 + 20

Pass Marks: 24 + 8 + 8

Time: 3 Hours

Candidates are required to give their answers in their own words as far as practicable.

The figures in the margin indicate full marks.

Section A

Attempt any TWO questions

1. Show that, For any NFA N=(Q, ∑, δ, q0, F) accepting language L=∑, There is a DFA D= (Q’, ∑’, q0′, δ’, F’) accepting the same language L.

2. State and prove the Pumping Lemma for regular languages. How can you show with an example that the pumping lemma is used to prove that a given language is not regular? Explain.

3. Given the following expression grammar for simple arithmetic expression with operators + and *.

                   E → E+T | T
                   T → T+F | F
                   F → (E) | a
               

   Remove the left recursion from this grammar then simplify and convert to CNF.

Section B

Attempt any EIGHT questions

1. Explain the ε-closure of states on an ε-NFA with suitable examples.

2. Convert the following regular expression into equivalent Finite Automata

   1. (0+1)*10(1+0)
   2. 1*0(0+1)*1

3. Define the term: Parse Tree, left-most and right-most derivation, sentential form, and ambiguity with an example.

4. Give the formal definition of Push Down Automata. How CFG can be converted into an equivalent PDA. Explain with an example.

5. Define regular grammar. Also explain the method of converting right linear grammar into an equivalent finite automaton.

6. Construct a Turing machine that accepts the language, L = {an bn | n≥0}

7. Define Turing machine and its roles.

8. Explain about the complexity classes p, NP, and NP-Complete.

9. Write short notes (Any two):

   1. Big Oh, Big Omega, and Big Theta
   2. Tractable and Intractable Problems
   3. Chomsky Hierarchy