b-tech sem-6 (ce-it) =2012

3
MaxTime:3Hour] Instructions: Seat No GANPAT UNIVERSITY B.Tech. Semester \4 Examination May-June - 2012 C8601/IT601 : Theory of ComPutation [Total Marks : 70 1. Al1 questions are comPuisorY 2, Figures to the dght indicate firll marks. 3. Answer Both Sections in Separate Answer sheets Q-1 IAl SECTION-I Answer the following questions. Let M\ and M2 be the FAs pictured below accepting languages Ll and L2, respectively. DrawFAs accepting thefollowinglanguages' a.LltJ L2 b.L1 nL2 c.L7-L2 'ridr t6t Findtheregular expression on alphabet {0, i} for followinglanguages' 1. The'language ofall stringiin whichnumber of0's is even and the number of I's is odd. 2. The language of all strings does not end with 01 ' 3, The language of all string not containing the substring 00' a.Thelanguageofallstringsinwhichevery0isfollowedimmediatelybyll. 5. The language of all strings havinglength6 or iess' 6. The language of all string not containing the substring 000 IOR] Answer the following questions. DrawDFA for followingRegular Expressions. 1. (a+b)* (b+ aa) (a+b)* 2. (bbb+ baa)*a Answer the following questions. 1. If R= I(1,2),(2,1),(l,l),(2,2)\ be a relation on set { 1,2,3 }' Of thethree ptop"J". i"n"tivity, symmetry, transitivity determines which ones the relation R has. Givereason. 2. Prove D'Morgan I a''"'' using VennDiaglans' 3. Write Quantified Statement for P is PrimeNumber' [6] tBl Q-r IAl t6l I61 IB1 '/,t. P.T.O.

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Page 1: B-Tech SEM-6 (CE-IT)  =2012

MaxTime:3Hour ]

Instructions:

Seat NoGANPAT UNIVERSITY

B.Tech. Semester \4 ExaminationMay-June - 2012

C8601/IT601 : Theory of ComPutation

[Total Marks : 70

1. Al1 questions are comPuisorY2, Figures to the dght indicate firll marks.3. Answer Both Sections in Separate Answer sheets

Q-1

IAl

SECTION-I

Answer the following questions.

Let M\ and M2 be the FAs pictured below accepting languagesLl and L2, respectively. Draw FAs accepting the following languages'

a .L l t J L2 b .L1 nL2 c .L7-L2

'ridr

t6t

Find the regular expression on alphabet {0, i} for following languages'

1. The'language ofall stringi in which number of0's is even and the number of

I's is odd.2. The language of all strings does not end with 01 '

3, The language of all string not containing the substring 00'

a.Thelanguageofal lstr ingsinwhichevery0isfol lowedimmediatelybyl l .5. The language of all strings having length 6 or iess'6. The language of all string not containing the substring 000

IOR]Answer the following questions.Draw DFA for following Regular Expressions.

1. (a+b)* (b+ aa) (a+b)*2. (bbb + baa)*a

Answer the following questions.

1. If R= I(1,2),(2,1),(l,l),(2,2)\ be a relation on set { 1,2,3 }' Of the three

ptop"J". i"n"tivity, symmetry, transitivity determines which ones the

relation R has. Give reason.2. Prove D'Morgan I a''"'' using Venn Diaglans'3. Write Quantified Statement for P is Prime Number'

[6]tBl

Q-rIAl t6l

I61IB1

'/,t.

P.T.O.

Page 2: B-Tech SEM-6 (CE-IT)  =2012

Q-2tAl

tsl

I61IB1

Answer the following questions,Draw FA using KLEEN's theorem part- I for

{* + &f {o&&o* + {et)*&{?itBl For a given regular expression draw NFA-Null aad convert it into DFA

((00*)* 1)*

IOR]Answer the following questions.Draw FA using KLEEN's theorem part-i for

(0 +r)* (011 + 01010) (0 + 1)*

For a given regular expression draw NFA-Null and convert into DFA

{rt*&b}* * S&*o*

Answer the following questions.For the following FA find a rninimum state FA recognizing the same ranguage with anecessary steps.

Q-2tAl

Q-3IAl

I4ltBl

t3l

tsl

Prove using PMI that for every n > 0 ,

T1 aLrtt*r:

"+1LetL= { wvr/we {0, 1}* ;showthatL is regular or not using pumping lemmatheorem.

T

ICI

P.T.O

Page 3: B-Tech SEM-6 (CE-IT)  =2012

SECTION.IIQ.4 Answer the following questions.

lAl Convert given CFG to Chomsky normal form (CNF)S- -+ IU IY

7' ---> cTIa I h

U ----+ cU I A

Xr -e. rrVc I IV

l4 . - -+b l { ' lA

lBl Prove that given CFG is ambiguous or notS)aSb laaSb l "

lcl Prove using Pumping lemma that following language is CFL or not?

L= { a 'U ck I k>nandk> j }toRl

Q,4 Answer the following questions.

lA1 Convert given CFG to Chomsky normal form (CNF)S) AaA ICA lBaBA) aaBa I CDA I aa IDCB tbB lbAB {bb lasC) Ca lbC lDD) bD l "

lBl Prove that given CFG is ambiguous or notS)a lSa lbSSlSSb lSbS

lcl Prove using Purnping lemma that follot'ing language is CFL or not?

L : { and ck i k= j *n }Q-5 Answer the following question

lAl Design PDA for {xe {a,b}*/ N"(x): 2N(x) }. Trace for sample val id and

invalid input strings.

lBl Prove using Pumping lemma that following language is is CFL or not?

L : {ww/We{a ,b } * }

t6l

t3l

13l

t6l

Q-sIA1

IBI

IOR]Answer the following questions.Design PDA for {xe{a,b}x / N"(x): Nr(x)+1}. Trace for sample val id andinvalid input strings.Prove using Pumpilg iemma that following language is CFl. or not?L : {WW"/We{ab} * }

t3l

t31

t6l

i51

161

tst

Q-6 Answer the following questions.

tAl write non deterministic PDA for given cFG. Converl Non deterministic PDA

deterministic PDA by using look aheads (LA). Trace the string for both PDA'S 'T$T) [T ]T l ^

lBl Design Turing Machine to copy given input string.

to t6l

t6l

END OF PAPER