CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
OCTOBER15
ASSESSMENT_CODE MC0082_OCTOBER15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
5146
a.Explain the five ways to describe a set.
QUESTION_TEXT
b.What is the value of
c.Define Deterministic Finite Automata.
a.(5 marks)
i.Describe a set by describing the properties of the members of the set.
ii.Describe a set by listing its elements.
iii.Describe a set A by its characteristic function.
iv.Describe a set by recursive formula. This is to give one or more
elements of the set and a rule by which the rest of the elements of the
set may be generated.
v.Describe a set by an operation (say union, intersection, complement
etc ) on some other set.
SCHEME OF
EVALUATION
b.=(1/2)+(2/3)+(3/4)=23/12 (2 marks)
c.A DFA is 5-tuple or quintuple M=(Q, Σ, δ, q 0, F) where
Q is non-empty, finite set of states
Σ is non-empty, finite set of input alphabet
Δ is transition function, which is mapping from Q x Σ to Q. for this
transition function the parameters to be passed are state and input
symbol.
Based on the current state and input symbol, the machine may enter
into another state.
q 0∈Q is the start state.
F⊆Q is set of accepting or final state.
(3 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
5148
QUESTION_TEXT
a.Explain the concept of grammars and languages.
b.What do you mean by a transition graph? Explain.
c.Explain the need for non-deterministic finite automata.
a.
A Language L can be considered as a subset of the free monoid on an
alphabet. It is a set of strings or sentences over some finite alphabet.
Finite languages can be specified by exhaustively enumerating all their
sentences.
A Grammar is defines by a 4–tuple G=(V N, V T, S, ϕ) where S is a
distinguished element of V N called the starting symbol), ϕ is a finite
subset of the relation from
(V T∪V N)*V N(V T∪V N) to (V T∪V N)*
A simple method of specification which satisfies this requirement using
general devices is referred to as grammar.
SCHEME OF
EVALUATION
b.A finite directed labeled graph in which each node or vertex of the
graph represents a state and the directed edges from one node to another
represent transition of state. All the edges of the transition graph are
labeled as input/output.
c.Digital computers are deterministic machines. Given the input, the
state of the machine is predictable. Sometimes, constructing
deterministic machine is difficult compared to non-deterministic
machine. In such cases, there is a need to construct a machine very easily
which can be achieved by constructing a NFA. After constructing NFA,
DFA can be easily constructed. This is an efficient mechanism to
describe some complicated languages concisely. So, practically nondeterministic machines will not exist. But one can construct an NFA
easily and later that can be converted into DFA.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
5149
QUESTION_TEXT
a.Explain the algebraic operations defined with regular expression.
b.Prove that if L is regular and f is homomorphism then homomorphic
image f(L) is regular.
SCHEME OF
EVALUATION
a.
● Union: The union of two regular expressions is also a regular
expression. For example if R 1 and R 2 are the two regular expressions
then the union R 1+R 2 is also a regular expression.
● Concatenation: The concatenation of two regular expressions is a
regular expression. For example if R 1 and R 2 are the two regular
expressions then the concatenation R 1R 2 is also a regular expression.
● Iteration: The iteration of a regular expression is also a regular
expression. For example if R 1 is a regular expression, then the iteration
R 1* is also a regular expression.
● Order of evolution: The order of evolution of a regular expression is
a regular expression. For example, if R 1 is a regular expression, then
order of evolution (R 1) is also a regular expression.
b.
Let R be the regular expression and L(R) be the corresponding regular
language. We can easily find f(R) by substituting f(a) for each a ∈Σ.
By definition of regular expression, f(R) is a regular expression and so
f(L) is regular language. So, the regular language is closed under
homomorphism.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72484
QUESTION_TEXT
Explain the various types of grammars in detail
Solution:
Explanation of:
2 x5 = 10 Marks

Type 0 grammar or unrestricted grammar

Type 1 grammar or context sensitive grammar

Type 2 grammar or context free grammar

Type 3 grammar or regular grammar
SCHEME OF EVALUATION
Monotonic grammar
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
109987
QUESTION_TEXT
Briefly explain how to convert NFA to DFA.
Explanation (4 marks)
SCHEME OF EVALUATION
Example + explanation (3 + 3 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
109991
QUESTION_TEXT
Prove that “The number of vertices of odd degrees is always even”.
We know that some of degrees of all the ‘n’ vertices
(say,
So we have
of a graph G is twice the number of edges (e) of G.
----- (i)
If we consider the vertices of odd degree and even degree
separately, then
SCHEME OF
EVALUATION
----- (ii)
Since the L.H.S of (ii) is even (from (i)) and the first expression on the
RHS side is even, we have that the second expression on RHS is
always even. Therefore,
----- (iii)
is an even number.
In (iii), each d(vk) is odd. The number of terms in the sum must be
even to make the sum an even number. Hence the number of vertices
of odd degree is even.