Following Paper ID and Rolr No. to be filled in your Answer Book
B.Tech.
(sEM. Vrr) THEORY EXAMTNATTON 20n _12 COMPUTATIONAL COMPLEXITY Time
: 3 Hours
Total Marks
:
lA0
Note :Attempt all questions.
L
Attempt any two parts of the following
(a)
(10x2:20)
:
What are the different models of computation ? Describe these models in comparative manner.
(b)
Prove or disprove the following conjectures
:
(D f(n): o (g(n)) implies o (f(n)) (ir) f(n) + g(n):0 (min(f(n), g(n))) (iiD f(n): o (g(n)) implies s(n) =
2f
@)

O(2er,l;
where f(n) and g(n) are asymptotically positive functions.
(c)
Are the following sets closed under the following operation. Prove your answer
(i)
FIN (the set of finite languages) under the function odds L, defined on languages as follows : odds (L)
(ii)
:
:
{w
:
!
x e L(w: odds(x)))}.
INF(the set of infinite languages) under the function odds L.
ECS0T2KLH26644
I
[Turn Over
2.
Attempt any two parts of the following
(a)
:
(10x2=20)
What do you mean by complexity classes ? Discuss the relationship among the complexity classes.
(b) Show that if there is a reduction from P, to P, then (i) If P, is undecidable then so is P.. (ir) If P, is nonrecursive enumerable then so is P,. (c) State and prove Rice theorem. :
3.
Attempt any two parts of the following
:
(10x2=20)
(a) Explain the general steps in establishing NPcompleteness proof of
(b)
a given problem.
Explain the Gddel's incompleteness theorem with the help
of examples.
(c) 4.
Write the randomized version of Quick sort algorithm.
Attempt any two parts ofthe
following:
(a) State the circuit satisfiability
(10x2=20)
problem. Prove the circuit
satisfiability problem belongs to the class NP.
(b)
Consider the problem of multiplication of an nxn matrix
A
:
(aij) by an nvector
Y: 0i) is given Yi =
\n
f
x = (x,). The resulting nvector
bY the equation
au x,
;
:
for i=7,2,
"",n.
j=r
Write an al gorithm to perform matrixvector multipl i cation by computing all the entries
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terms Pixel, Aspect Ratio, Resolution. O) Develop and write mid point circle algorithm. Apply it to. predict the pixels in any octant for the circle whose centre.
There was a problem loading more pages. Retrying... Whoops! There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. UPTU B.Tech Pattern Recognition ECS074 Sem 7_20
(e) Enumerate the 'advantages of the layered. approach to system design? Also, Explain. virtual machine architecture in detail. (0 What are Sernaphores?
4. Attempt any two parts of the following : (10x2=20I*. (a) Explain Issues ofRecovery in distributed database. Explain. types of failure in distributed system.
OPERATINGSYSTEM. Time : 3 Hours ... favour of the oldest process. Draw the Gantt ... Displaying UPTU B.Tech Operating System ECS501 Sem 5_201314.pdf.