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Fifth Semester B.E. Degree Examination, Dec.2017/Jan.29;18 Automata Theory & Compatibility' . Time: 3 hrs,

.'

Max. Marks: 80

co m

<

.

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)

I of3

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.""\

3

\

~,,'." bet L be the language

accepted

,..... - .... \ '.

by the following

(04 Mar

finite state machine.

b

,

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f, .'

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

lo g. co m

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

1/;;

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, [email protected]'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

«\~y

'-..." 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

/.

.J

ik

a. b. c.

V'

'v

w

-,

,,***** ,,>}

",-,'

.;'-

/"

. )' 1 -- /

w w

w

.p

ed

ia

"

\

(/ ./

-.

,' -,,' 'J

3 of 3

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(16 Marks)

## Automata Theory Jan 2018 (2015 Scheme).pdf

Explain the-following terms: (i) (,; Pushdown automata (PDA). (u)' Languages of a PDA. ~ Qii)/ Instantaneous description of a PDA.

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