Bachelors Level/Second Year/Fourth Semester/Science csit/fourth semester/theory of computation/syllabus wise questions

B.Sc Computer Science and Information Technology

Institute of Science and Technology, TU

Theory of Computation (CSC262)

Year Asked: 2079, syllabus wise question

Basic Foundations
1.
Explain the ε\varepsilon-closure of states on an ε\varepsilon-NFA with suitable examples. [5]
2.
Write short notes (Any two): a) Big Oh, Big Omega and Big Theta b) Tractable and Intractable Problems c) Chomsky Hierarchy [5]
Context Free Grammar
1.
Given the following expression grammar for simple arithmetic expression with operator + and *. Remove the left recursion from this grammar then simplify and convert to CNF.
EE+TTE \rightarrow E+T \mid T
TT+FFT \rightarrow T+F \mid F
F(E)aF \rightarrow (E) \mid a
[10]
2.
Define the term: Parse Tree, left-most and right-most derivation, sentential form and ambiguity with example. [5]
Introduction to Finite Automata
1.
Show that, for any NFA N=(Q,Σ,δ,q0,F)N = (Q, \Sigma, \delta, q_0, F) accepting language L=ΣL = \Sigma, there is a DFA D=(Q,Σ,q0,δ,F)D = (Q', \Sigma', q_0', \delta', F') accepting the same language LL. [10]
Push Down Automata
1.
Give the formal definition of Push Down Automata. How CFG can be converted into equivalent PDA. Explain with an example. [5]
Regular Expressions
1.
State and prove the Pumping Lemma for regular languages. How can you show with example that pumping lemma is used to prove that a given language is not a regular? Explain. [10]
2.
Convert the following regular expression into equivalent Finite Automata.
a.(0+1)10(1+0)a. (0+1)*10(1+0)
b.10(0+1)1b. 1*0(0+1)*1
[5]
3.
Define regular grammar. Also explain the method of converting right linear grammar into equivalent finite automata. [5]
Turing Machines
1.
Construct a Turing machine that accepts the language,
L={anbnn0}L = \{a^n b^n \mid n \geq 0\}
[5]
2.
Define Turing machine and its roles. [5]
Undecidability and Intractability
1.
Explain about the complexity classes p, NP and NP-Complete. [5]