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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
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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.
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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.
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{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)
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