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PROGRAM-BACHELOR
OF COMPUTER APPLICATION
SEMESTER-5TH
SEM
SUBJECT
CODE & NAME
BC0052
– THEORY OF COMPUTER SCIENCE
CREDIT-4
BK
ID-B0972
MAX.
MARKS-60
Q.1.
Define g.c.d. (m,n) Solve recursively: (i) f(x, y) = x + y, (ii) g(x, 0) = 0,
g(x, y + 1) = g(x, y) + x. [3+3.5+3.5] =10
ANS:
Definition: If m and n are two non-negative
integers then the (greatest common divisor) g.c.d. (m, n) is defined as
the largest positive integer d such that d divides both m and n. Euclidean
algorithm computes the greatest common divisor (g.c.d.) of two non
negative integers.
Q.2.
Obtain a DFA to accept strings of a’s and b’s starting with the string ab. [10]
=10
ANS:
A
DFA to accept strings of a’s and b’s starting with the string ab.:
Solution: It is clear that the string should
start with ab and so, the minimum string that can be accepted by the
machine is ab. To accept the string ab, we need three states and the
Q.3.
Prove by mathematical induction. [10] =10
ANS:
Solution:
Q.4.
Briefly describe Moore and Mealy machines. [10] =10
ANS:
Moore and Mealy Machines: The automaton systems we have
discussed so far are limited to binary output. That is, the systems can
either accept or do not accept a string. In those systems, this
acceptability is decided based on the reachability from the initial
state to the final state. This property of the system produces restrictions
in choosing outputs from some other alphabet, then output. You
Q.5.
If G= ({ S}, { S->0S1, S->^}, S)
t then find L(G), the language generated
by G. [10] =10
ANS:
Solution:
Since S®^ is
a production, S=>^. This implies that ^ € L(G)
Now, for all n≥1, we can write
the following:
S=>0S1=>00S11...=>0nS1n
=> 0n1n
Q.6.
Prove that “A tree G with n vertices has (n–1) edges” [10] =10
ANS:
Proof : We prove this theorem by induction on
the number vertices n.
Basic step:
If n = 1, then G contains only
one vertex and no edge.
Get fully
solved assignment, plz drop a mail with your sub code
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Charges rs 125/subject and rs
700/semester only.
our
website is www.smuassignment.in
if urgent then call us on
08791490301, 08273413412
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