CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
JULY15
ASSESSMENT_CODE BC0052_JULY15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
5987
QUESTION_TEXT
Explain the steps involved in conversion of Mealy Machine into Moore
Machine.
SCHEME OF
EVALUATION
Step1: For a state q i determine the number of different outputs that are
available in θ state table of the Mealy machine. (2 marks)
Step2: If the outputs corresponding to state q i in the next state columns
are same, then retain state q i as it is. Else, break q i into different states
with number of new states being equal to the number of different outputs
of q i. (2 ½ marks)
Step3: Rearrange the states and outputs on the format of a Moore
machine. The common output of the new state table can be determined
by examining the outputs under the next state columns of the original
Mealy machine. (2 ½ marks)
Step4: If the output in the constructed state table corresponding to the
initial state is 1, then this specifies the acceptance of the null string ^ by
Mealy machine. Hence to make both Mealy and Moore machines
equivalent, we either need to ignore the output corresponding to the null
string or we need to insert a new initial state at the beginning whose
output i s0. The other row element i this case would remain the same. (3
marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
5988
QUESTION_TEXT
Explain the algebraic operations defined with regular expressions.
Explain by taking two regular expressions say R1 and R2. Give
recursive definition for regular expressions.
SCHEME OF
EVALUATION
Union: The union of two regular expressions is also a regular
expression. For example, if R1 and R2 are two regular expressions, then
the union R1 and R2 is also a regular expression. (1 mark)
Concatenation: The concatenation of two regular expressions is a
regular expression. For example, if R1 and R2 are the two regular
expressions, then the concatenation R1R2 is also a regular expression.(1
mark)
Iteration: The iteration of a regular expression is also a regular
expression. For example, if R1 is a regular expression, then the iteration
R1* is also a regular expression.(1 mark)
Order of evolution: The order of evolution of a regular expression is a
regular expression. For example if R1 is a regular expression, then order
of evolution (R1) is also a regular expression. (1 mark)
A regular expression is recursively defined as follows.
1.ϕ is a regular expression denoting an empty language.
2.^ is a regular expression which indicates the language containing an
empty string.(1 mark)
3.a is a regular expression which indicates the language containing only
{a}.(1 mark)
4.If R is a regular expression denoting the language L R and S is a
regular expression denoting the language L S. Then
a.R + S is a regular expression corresponding to the language L R L S.
b.R . S is a regular expression corresponding to the language L R . L S .
c.R* is a regular expression corresponding to the language L R.(3
marks)
5.The expressions obtained by applying any of the rules from 1 to 4 are
regular expressions.(1 mark)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72470
QUESTION_TEXT
Prove that
for any integer n and real x.
Solution: Case i: The proof is clear when x is an integer.
Case ii: Suppose that x is any real. Then
--.-- (i)
SCHEME OF
EVALUATION
Also for any real x, and integer n, x + n <
(ii)
From (i) and (ii)
+n x+n<
+n+1
+n + 1
-----------
-------- (iii)
Take k =
+ n and y = x + n
Then (iii) becomes k y < k + 1, is real and k is an integer
By rule (1) of 4.5.7, we get
That is,
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72474
=k
(10 marks)
QUESTION_TEXT
Explain the operation of finite automaton in detail. Differentiate
between deterministic finite automaton & non-deterministic finite
automaton.
SCHEME OF
EVALUATION
Operation of finite automaton (last para)
Strings are fed in to ……….internal states (1 mark)
This black box is …….initial state (1 mark)
At regular intervals ………next tape square (1mark)
This process is …….set of strings it accepts (2 marks)
Difference (Table)
1st difference (2marks)
2nd difference (2 marks)
3 & 4th difference (1/2 mark each)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
110658
Define each of the following with an example.
a.
Subset
b.
Union
c.
Cartesian product
d.
Power set
e.
Equal sets
QUESTION_TEXT
a.
Subset: A is a subset of B if every element of A is also an
element of B.
Ex: IF A={1, 2, 3}, B={1, 2, 3, 4}, then A⊆B
SCHEME OF
EVALUATION
b.
Union: IF A and B are two sets, then the set {x|x∈A or x∈B or
both} is union of A and B.
Ex: If A={1, 2, 3}, B={3, 4, 5} then A∪B={1, 2, 3, 4, 5}
c.
Cartesian product: If S and T are two sets, then the set {(s,
t)|s∈S and t∈T} is called the Cartesian product of S and T.
Ex: If X={a, b}, Y={x, y}, then X×Y={(a, x), (a, y), (b, x), (b,
y)}
d.
Power set: Let A be a set. The set of all subsets of A is called
the power set of A.
Ex: If A={1, 2}, then P(A)={∅, {1}, {2, }, {1, 2}}
e.
Equal sets: Two sets A and B are said to be equal if A is a subset
of B and B is a subset of A.
Ex: A={1, 2}, B={1, 2}, then A=B
(Each definition with example carries 2 marks)
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
QUESTION_TEXT
110659
Explain proof techniques in detail and mention special proof
techniques.
(5 + 5 = 10 Ans: Proof techniques: A significant for reading this subject
is the ability to follow proofs. In mathematical arguments, we employ the
accepted rules of deductive reasoning, and many proofs are simply a
sequence of such steps:
(i)
Direct Proof
(ii)
Indirect Proof
Special proof techniques are used to are:
SCHEME OF
EVALUATION
a.
Proof by induction
b.
Proof by contradiction
c.
The pigeonhole principle
d.
The Digitalization Principle
e.
Exhaustive Proof and proof by cases
Marks)