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USN

Fifth Semester B.E. Degree Examination, Dec.2015 IJan.20l6

Formal Languages & Automata Theory Time: 3 hrs.

Max. Marks:100

la.

co

(85 Man'ks) What is Automata? Discuss why study automata. (04 Nlarks) Mention the differences between DFA, NFA and NFA-c . Design a DFA to accept the language L = {W/W is of even length and begins with 01}.

b.

d

d .J I

d.

:r)

Design the NFA-e or NFA for the languages given below: i) abe, abd and aacd {Assume l: a,b,c,d }

ii) lab,abclx {Assume [=a,b,c]

boP X2 d9

,,

2 a.

Covert the following NFA-e to DFA using "subset construction sclxeme"

.g& eO

6;;

!O

ia

i) ;=1a2nb2-:n>0, m>0) ii) Language over {0, 1} having all strings not containing Convert the regular expression (0+1).1(0+l ) to a NFA-e

-+A

B

A

cno

B

A

C

O= F>

C

D D D G

B A

w w

o.= >1 (F

o

w

U<

o

o. E

{
E F

G

o o

Z P

{08 Marks)

(06 NIarks)

regular

languages.

Show

that

(08 h{arks) (04 Manks)

F 1.,

tl

D F-ig. Q3 (c)

F{

D ii)

F'

(06 N{arks)

00.

.

a. State and prove pumping Lemma theorem for I = {a"b' ln > 0} is not regutrar. b. What is Homomorphism? Explain with an example. c. Consider the transition table of DFA given below: 01

.p

oj ?-Y

($4 Marks)

Fig. Q2 (a) Define Regular expression and write regular expression for the following languages:

ed

b. c.

qc-

Marks}

w

*-

o€

{&6

ik

io

oO (dO -k

g.

O

PART _ A

lo

o

ib

a)

m

Note: Answer FIVEfull questions, selecting at least TWG questionsfrom ewck pat't.

G

Draw the table of distinguishabilities of states. Construct the equivalent minimized DFA.

ofL For More Question Papers Visit -1www.pediawikiblog.com

{08 *4arks)

For More Question Papers Visit - www.pediawikiblog.com 10cs56 Obtain a grarmnar to generate integers and write derivation for the unsigned integer 1965. (08 Marks) Consider the grammar:

-+

aS I aSbS le

.Is the above grannma.r ambiguous? Show that the string aab has two i) . Parse frees ii) Left most derivations iii) Rightmost derivations

PART _ B

b.

Define pDA. Design PDA to accept the language L(M) = state and also give the graphical representation of PDA. Convert the follorving CFG to PDA:

S+aABBlaAA

lr,r e (a

* b)-} by a final

lo

A -+ aBts la

B+bBBlA

(tr2 Marks)

Consider the fcrllowing grammar:

S+AStsle

ik

A+aASla E+SbSlAlbb

(08 Marks)

ib

C-+a

6a.

{*a*o

(12l\{arks}

g.

5 a.

-

m

S

co

a. b.

i)

C.

and also write its transition

b.

Explain

ttrLe

diagram.

(12 Marks) general structure of multitape and non deterministic turing machines. (08 Marks)

w

w w

I

(08 Marks)

Design a ttring machine that perf,orms the following function: *qrcoo for any rrl e {1} x eoo l*

.p

7 a.

ed

b.

ia

w

Are there any useless symbols? Eliminate if so. ii) Eliminate e productions. iii) Eliminate unit productions. iv) Fut the grarnmar into Chomsky Normal Form. (08 IVIarks) Show that L = {anbnc' in > 0} is not context free. (S4 Marks) Frove thattthe context free languages are closed under union, concatenation and reversal.

a. b. c. d.

Write short notes on: Applications of regular expressions. Applications of context free Grammars. Fost's correspondence problem. Chomsky hierarchy.

(20 Marks)

,FA**r,<

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