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Fifth Semester B.E. Degree Examination, Dec.2017/Jan.29;18 Automata Theory & Compatibility' . Time: 3 hrs,
FIVEfull ote: Answer . 1
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Max. Marks: 80
co m
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.
questions, choosing one full question/rom 'each module. ..
" Module-l Define the fo llowing terms with examples: (i) Alphabet (ii) Power of an alphabet (iii) Concatenation (iv) Languages (04 Marks) Draw a DFA to accept strings of a's and b's ending with 'bab' _ ,', (03 Marks) Convert the following NDF M Fig. Q I (c) to its equivalentl)FSM. (09 Marks)
a.
lo
g.
b. c.
Fig. QI (c)
OR Draw a OF M to accept the language,
b.
L = {w E {a,b '
r:
ib
a.
r
Marks)
rs-ro--T -
ik
2
B A A C D Bt D AI 0 F' G E
G
F G
aw
.A B C *0 E F
a.
di
w
3
II 0 (i) Draw the table ofdistinguishable and indt tinguishahle state for the automata. (09 Marks) (ii) Construct minimum tate equivalent of automata. Write differences between DFA, FA and E- FA. (04 Marks) Module-2 Consider the DF A shown below:
.p e
c.
G
3
w w
Obtain the regular expres ions R,/o, R'J possible.
2
o c
~ o
0.
E
b.
is
and simplify the regular expressions
!)
z
I
>.
Give Regular expressions for the following languages on (i) (ii)
all strings containing exactly one a all strings containing no more than 3 a's.
(iii)
all string
I =- {a, b.c]
that contam at least one occurance of each symbol in
much.as
(O~..Mllrks)
I
.
(03 Marks)
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3
\
~,,'." bet L be the language
accepted
,..... - .... \ '.
by the following
(04 Mar
finite state machine.
b
,
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Fig. Q3 (c) l~r each of the following
(i)
(a (;
.
regular
expressions,
whether
(ii)
(€,u~b)a(bb * a) *
(iii)
bauabl4
(i)
(aub'a)(bb*a)*
. a.
\
OR
Prove that the following
Jarig~1age in not regular: \, " . L2 are regular languages then prove
b.
If LI and
c.
languages. Is the following S ~ iC + S I iC
that
LJ uL2,
Ll.L2 and
grammar + SeS I a
is ambiguous? ,
"
(06 Marks)
,
B~SbSIAlbb Let G be the grammar,
' .)
r...
bA aSJ bAA
(09 Marks)
w
B~blbSlaBB
(03 Marks)
for each.
ib
Define Grammar, Derivation, Sentential forms and give one example What is CNF? Obtain the following grammar In CNF S~ASBIE A~aASla
S ~aBI A ~al
L'J are regular
ik
c.
(05 Marks)
.~
'
(05 Marks)
Module-3 a. b.
,
a.
\.
/
\.
ed
.......
ia
For the string aaabbabbba find a (i) Left most derivation, (ii) Rigti~most derivation, (iii) Pats~iree. , -
6
Explain the-following (i) (,; Pushdown (u)' Languages
b. _,S::~n~tr'uct a PDA
(04 Marks)
OR
terms: automata (PDA). of a PDA.
Instantaneous
.p
~ Qii)/
L:
,
L = {onI 11'1 n > O}. I
C~b
5
describes
ba )bb * a
/
4
it correctly
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Indicate
to
description
accept
the
of a PDA. language
L
= ~WR
IW
E
{a, b}'}.
Draw
Marks)
the' graphical
w w
w
representation ofthi PDA, Show the moves made by this PDA for the string aabbaa. ----~-~ (10 Marks) c. Convert the following CFG (0 PDA S~aABBlaAA
A~aBBla
B~
bBBIA
c-»
(03 Marks)
2 of3
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I 7
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Module-4
!l-:-::::I.f;L1 and L2 are context free languages then prove that LI U L2' L\ . L2 and L"I~
~ntext
6
n(; ,ATe~~anguages. b. vG~ __ a.decision procedure to answer each of the following questions: \' ..{1) "Given a regular expression a and a PDA M, the language accep~~ M a subset .r.: "Ir--i· (", 0¥ the language generated by a? r: v <~/ (ii), ,)Given a context-free Grammar G and two strings SI and S2, d@s'J1 generate S,S2? (iii)\~9iV~Q a context free Grammar G, does G generate any even.))e..~ strings. (iv) 'G~v..e',t a Regular Grammar G, is L(G) context-free? . ' (12 Marks) 04 Marks)
(,
{
/..;\\.
/~',
v~"
. ~ OR (OS Marks) Explain with nea~ ~i~&ram, the working of a Turing Machine ~j9r Design a Turing mic~~\ to accept the language L = {a I} . Draw the transition diagram. Show the m(1f~~~ade by this turing machine f<;R~e\s'tring aabbcc. (11 Marks)
»>: '
<"''//,:; :
8
:
lo g. co m
,~\@
a.
n~~~J?{>=
b.
' --;>!->~.'>
\'"
\
a. b. c.
-..
'
1,/'·....... r ,
-II
...),- .•
e .
(16 Marks)
ib
9
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'-..." Module-5 ..," Write short notes on: ( (' ,; I--::'I.~~""·) Multi-tape turing machine, '--\.) ~ '.Q.()/ ~>Y'l;:/' Non-deterministic turing machille:; . "-./ \ / Lmear Bounded automata. ,:: .-/ r::'\... \,/ '-
/
" /i{)R '. ~'
"
Write short notes on: Undecidable languages. Halting problem ofturing machine. . The post correspondence problem"
10
/.
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ik
a. b. c.
V'
'v
w
-,
,,***** ,,>}
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.;'-
/"
. )' 1 -- /
w w
w
.p
ed
ia
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(/ ./
-.
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(16 Marks)
