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Roll No. I. I I I I I I I I I I I
S. No. ofQuestionPaper 6075 Unique Paper Code Name of the Paper Name of the Course Semester
Theory of Computation (CSHT-511) : B.Sc. (Hons.) Computer Science :V
D
Duration : 3· Hours Maximum Marks : 75 (Write your Roll No. on the top immediately on receipt of this question paper.) Question No. 1 (Section A) is compulsory. Attempt any four questions from Section B. Parts of a question should be attempted together. Assume L = {a, b} for all the questions unless specified otherwise. Section A
1. (a) Is for all sets (S+) * = (S*)+?
(b) Generate a CFG for a* b*.
(c). Give Regular expression for all words that do not end in a double letter. 2
P.T.O.
(d) Defme Deterministic Finite Automata 2
(e) Design a Deterministic Finite Automata for all strings that either starts with ab or ends
with ba. 3
(j) Give the full details of the following Turing Machines : 3
L Land > L u^ R
. (g) Convert the following Transition graph into Regular Expression. 4
(h) Convert the following CFG into CNF : (^4) S --7 bAiaB · A --7 bAA I aS I a B --7 aBBibSib
\
( 4 ) 6075
(b) Convert the given NFA into DFA. 5
·~^ .. ·.:.... __ ~~-.^ ~:··.>~+·..^ :· ,;^^ ::,.:·.,.·
3. (a) Build a DFA and give Regular Expression that define L 1 nL 2 where :
L 1 : (a+b) b (a+b)*
L 2 : b (a+ b)*. 6
(b) Show that the language :
is non Context Free. 4
4. (a) Show the Complement of the Context Free Language may or may not be Context
Free. 5
(
( 5 ) (^6075) (b) Show that the CFG is ambiguous : S -7 XaX
X -7 aXIbXI". <;
- (^) ({1) (^) Explain the Concept of Random Access Turing Machine. (^) }
(b) Explain Halting Problem._ 2
(c) (^) Give PDA for the language : L ={an b2n (^) where n = 1 2 3 .... }. (^6)
6. (a) Show that if Lis recursive, then L is also recursively enumerable. 4
(b) Design a Turing Machine which gives two's complement of a given input in binruy fl,nr
on the input tape. - 6
- (a) Describethe Language for the following R~gular Expressions : (^3) (i) (a+b)ab(a+b) (ii) (a(a + bb)*) * (b) Build a DFA that accepts all words with exactly four letters. (^3)
P.T.O.
