ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE …fmcet.in/CSE/CS6503(R-13)_auque.pdf · rejinpaul.com...

ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE

B.E./ B.TECH. DEGREE EXAMINATIONS: APRIL / MAY 2011

REGULATIONS: 2008

FIFTH SEMESTER: INFORMATION TECHNOLOGY

080250018 - THEORY OF COMPUTATION TIME: 3 Hours

PART-A

ANSWER ALL QUESTIONS

1. What is finite automaton? Give two examples.

2. Distinguish between NFA and DFA.

3. What is the language represented by set L(aa* + aba*b*)?

4. What is an automaton with output? Give an exa'mple.

5 Generate the CFG for the language L = {0*1*}.

6. What is meant by derivation?

7. Define the instantaneous descriptitln of PDA

8. Define GNF.

9. What is meant by Turing machine?

10. Define the Turing machine halting machine.

11. List out the techniques for Turing machine construction.

12. What is multiple track Turing machine?

13. Define recursive language.

14. When a language is said to be recursively enumerable?

15. State Rice theorem.

16. Mention any tow undecidaQility properties of REL.

17. Distinguish between time and space complexities.

18. Define NP - Complete problem.

19. What are tractable problem?

20. What is an intractable problem? Give two examples.

Max.Marks : 100

(20 x 2 = 40 MARKS)

www.vidyarthiplus.com


downlo

aded

from re

jinpa

ul.co

m

FMCET

PART - 8

(5 x 12 = 60 MARKS)

ANSWER ANY FIVE QUESTIONS

2 1. a) Prove the following by ciple of induction. prin.

6

1.1! + 2.2! +3.3! + ........... + n.n! = (n+1)!-1, n> 1.

b)Show that L = {On 10n I n≥1} is not regular 6

22.a) Discuss about the Chomsky hierarchy of languages. 4

b)Construct a NFA that accept the set of all strings {a, b} ending with "aba" as 8

substring and construct DFA.

23 a) Find a deviation tree of a * b + a * b given that a * b + a * b is in L(G), where 4

G is given by S → S + S, S → S * S, S → a / b

b) Find the CNF for the following grammar 8

" S → AS I as, A → aab IE, S → bba

24. a) Show that the language L = {an bn cn dn I n≥O} is not CFL 6

b) Discuss the models of Turing machines. 6

25 Design PDA for the language L = {a3n bn I n≥O} and simulate its action on

the input string aaaaaabb.

26. a) Show that the language L and its complement L' are both recursively 6

enumerable then L is recursive. b) Explain the halting problem Is it decidable or undecidable problem

6



downlo

aded

from re

jinpa

ul.co

m

FMCET

27.

Write a short notes on the following

a) Universal Turing machine

b) Post Correspondence Problem

6

6

28. a) Prove that a problem p2 cannot be solved in polynomial time can be proved 6

by the reduction of a problem p1, which is under class p1 to p2.

b)Write a note on NP - Completeness. 6

*****THE END*****

3



downlo

aded

from re

jinpa

ul.co

m

FMCET

www.rejinpaul.com

www.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.com

www.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.com









FMCET

www.rejinpaul.com

I

Reg. No.:

Question Paper Code z 6628L.,,iiii"" ""!lii:,;l:llll;i::'::r,,,'....

B.E, / B.Tech. DESREE ExAMINATISN, N9vEMBER/ DEcEfuER *o'1,;l .''nl ::: iii,'l'..r:i:

Fifth Semester

Time: Three hours Maximum: 100 marks

1.

2.

E.

4.

Computer Science and Engineering"t''it' .= ii::""u:'

'.;',,.:'CS 2303 -THEORY

OF COMPU.TATION,,,,,,,,,. 1:',,,,,,, ,,,,"ii"

', ,..,."::1.;,,.,. "a,'r,_,,, ,

(Common to Seventh Semester Information Teihnolqfl' :i"i::'

(Regulation 2008)

... l

Answer AL"L qrlestions''ti .:

PART A- (1,9, t 2, = 2O'marks)':::i., .,,0,*'

What is stmctural inductifin? *'*= .,,,,,,.,,_, ,';':"

State the difference NFA'and D-FA.

':t' j .l

Constmct a DFA for'tt'{eiifoll=owifig I j--'::l:.,. -.:

{a) Atl strings t}rat contain ABqlS 4 nros.

(b) All strings that don't contain the substring 11O'

Is the set of strings over the alphabet {O} of dre form 0n where n is not a

prime is :#ggtji?'Frore or disprove':]t-

':::; i:,i=! i::':':': s -+ss l(sls(s)slE ?,. Is the graTPaAUp,Xow,,ambiguousl

G;;;"th;"*ftflfloitirrg gr€rmmar into an equivalent

litp.dfircHons'iihpn$,:.:"*'and no useless symbols S '+ ABA

one with no unitA -+ aAAlancpt

ll;

8.

,'u'\,,.,+ lpfi lcb,G',:''-+ CCI cC .

r ''i .,i.'

."'.' ig" *lq]i that accepts the language of odd integers written in binary'

'''1,;'. ---r^State fiib two normal forms and give an example'

L I o I \ ) + O /+ 6

FMCET

9.

10.

How to prove tJ:at the Post Correspondence Problem is Undecidable'

Show that any PSPACE-hard language is also NP-hard'

PARTB-(5x 16*SOmarks)

Prove that JI is not rational'

Construct a DFA accepting all strings

the number of l's in ur is 3 mod 4'

11. (a) (4

ti1)

tltat

Or

fbl Construct a minimized DFA from 'thi' regular expresslon\-'

it*,)t(* + 'y)* ' Trace for a string v) = )ffyx ' '-r:;;::'

12.ta)StateandexplaintheconversionofDFAintoregularexpressionusingArden's theorem' fU""tt"[*itft an example' (16)

Or'',:, .

(b) (4 What are the clos-ure propefg oi re'Sillar sets?

(iil Define regular e4predSt-on' 8hoy that

tji (o *10 * l)= o * l(o + to * l)*(t +oo * 1;a(+--w''rxo+lo *=

.':.-.,i.

13. (a) (4 Is NP-DA tnfutt- 1'tinig ro4 andDPDA

equivalent? Illustrate ith an example'

(i4 What are tJ'e different typ": of lSguage

acceptances by a PDA

and define tt'"m' l" it tnie tfrat thJanguage accepted by a PDA

by theS. affer"nt types provides different languages? (8)

Or' a. :i:' :'::

"i'i,, ,,i.:'' nar S + qsbl A, AibSalSl€toaPDAthat

'Convert'the gramn

aecep'tstlresamelanguagebyemptystack.(10}

(rr)!, r,:"i-+a,SblsAb, A+bAa' A-+ba is the

'*ttj -' $"***. Determine the context free larrggage

::ir,:,. ,r:i:'

t8)

(8)

PDA)(8)

LF)' (1l

context free

(6)

662AL

FMCET

14. (a)

15. (a)

(b)

(il State the techniques for Turing machine construction?t-'

fllustrate with a simple language'

04 Explain the different models of Turing machines' (10)

or r,,,,.t''',

,._.,

td what are the closure properties of CFL? state th'e*ifi$'&..r $r,t''

t*o prop"rti"". ..:r-.:;;i:e,,-,. l:,, ,';i -

(u) state the Pumping lemma for cFL+' 'sfi+ry*ffiatn1-'

application? Give two examples' . ui'*''""'"'- 'l ::t-*#

':" :i l'

({ $tate t}re halting problem of T}vIs' *t*A* tQl tSb halting

problem orruringnrrLhine over {t:TF ae unsavafrei (8}

',,r,,,,,,,,,,,,,,".,,;l'

.

(iil ktl,={o'a}* ' l'et'Aand B he lists of ttrree"'Strings as given

below:

A = b, bab 3, ba\ B = \b3,.,,b&."d+,r,:::.,:::,:::::...

' "

Jotodo"a Justiff Yow ansm'er'(8)Does this instance otFCP&* -. :-

=w:,,,.,,.' .S* (8)

(8)(4

(ii)

'r..€1i:-la!,:-a 'il:.:'i;it'..*,,.::::

ri::::.

ti *,r,,:l!: :i,:,.i . r;Ir:i:... i!:

'";;:: ':r,....,:,r' i,:,::,, .,,

t? ':t:tr.:,. . ::''

3662AL

FMCET

Anna University

B.E/B.Tech DEGREE EXAMINATION APRIL/MAY 2008

Fifth Semester

Computer Science and Engineering

CS1303—THEORY OF COMPUTATION

(Regulation 2004)

Time: 3 hours Maximum marks: 100

Answer ALL questions

PART A (10 x 2 =20 marks)

1.Define Automaton?

2.What is the principle of mathematical Induction?

3.Construct a DFA for the regular expression aa*/bb*..

4.Construct a DFA over ∑=(a,b) which produces not more than 3 a’s.

5.Let S->aB/bA

A->aS/bAA/a

B->bS/aBB/b

Derive the string aaabbabba as left most derivation.

6. What is meant by empty production removal in PDA.?

7.State the Pumping lemma for CFG.

8. Define turing machine

9.What is meant by halting problem.

10.What is post correspondence problem?

PART B (5 x 16 = 80)

11. (a ) (i) Prove that for every integer n>=0 the number 42n+13n+2 is a multiple of 13

(ii)construct a DFA that will accept strings on{a,b}where the number of b’s divisible by 3

(or)

(b) (i) Construct a finite automaton that accepts the set of all strings in {a,b,c}* such that the last

downlo

ad fro

m www.re

jinpa

ul.co

m

FMCET

symbol in input string appears earlier in the string

12 (a) (i) Construct the regular expression to the transition diagram.

Diagram

(or)

(b)Construct a NFA for regular expression (a/b)*abb and draw its equivalent DFA.

13. (a) Construct a CFG accepting L={ambn/n

(or)

(b)Convert the grammar with productions into CNF A->Bab/λ.

14.(a) Design a deteministicturing machine to accept the language L={aibici/i>=0}

(or)

14. (b)Determine whether the language given byL={An2/N>=1} is a context free or not.

15. (a)Prove that the function fadd (x,y)=x+y

is a primitive recursive

(or)

15. (b)Show there existsaTM for which the halting problem is unsolvable

downlo

ad fro

m www.re

jinpa

ul.co

m

FMCET

www.rejinpaul.com

www.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.comwww.rejinpaul.com










FMCET

www.rejinpaul.com

ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE …fmcet.in/CSE/CS6503(R-13)_auque.pdf · rejinpaul.com...

Documents

Transcript of ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE …fmcet.in/CSE/CS6503(R-13)_auque.pdf · rejinpaul.com...