Download CUSTOMER_CODE SMUDE DIVISION_CODE SMUDE

CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
Jan2017
ASSESSMENT_CODE MC0082_Jan2017
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
5147
QUESTION_TEXT
Explain the concept of mathematical induction.
Let A be the set of all natural numbers such that
i.0∈A, and
ii.for each natural number n, if {0, 1, … , n}⊆A, then n+1 ∈A
Then A = N
SCHEME OF
EVALUATION
In other words:
The principle of mathematical induction states that any set of natural
numbers containing zero and with the property that it contains n+1
whenever it contains all the numbers up to and including n, must in fact
be the set of all natural numbers.
In practice, induction is used to prove the assertions of the following
form:
“For all natural numbers n, property P is true.”
The above principle is applied to the set A = {n:P is true of n} in the
following way.
a.In the basis step we show that 0∈A, i.e. P is true of 0.
b.The induction hypothesis is the assumption that for some fixed but
arbitrary n≥0, P holds for each natural number 0, 1, 2, … ,n.
c.In the induction step we show, using the induction hypothesis, that P is
true of n+1. By the induction principle, A is then equal to N, that is P
holds for every natural number.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72481
QUESTION_TEXT
Obtain a PDA to accept the language L={anb2n|n≥1}.
SCHEME OF
EVALUATION
The PDA to accept the given language is M = (Q, ∑, I’, δ, Z0, F)
where
Q = {q0, q1, q2}, q0 is the start state
∑ = {a, b}
Г = {a, Z0}, is the initial number of the stack, F= {q2} is the final
state. 5 Marks
The transitions δ are given by
5 Marks
δ(q0, a, Z0) = (q0, aaZ0)
δ(q0, a, a) = (q0, aaa)
δ(q0, b, a) = (q1, Λ)
δ(q1, b, a) = (q1, Λ)
δ(q1, Λ, Z0) = (q2, Λ)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
109984
QUESTION_TEXT
Explain Big Omega and Big Theta function with example.
Big Omega
Description (3 marks)
Example (2 marks)
SCHEME OF EVALUATION
Big Theta
Description (3 marks)
Example (2 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
109985
QUESTION_TEXT
Use the definition of order to show that, 5x 3 – 3x+4 is O(x 3)
The functions f and g referred to the definition of O-notation are
defined as follows.
For all real numbers
For all real numbers x > 1,
and
(by the triangle inequality)
SCHEME OF
EVALUATION
Therefore,
or
for all x > 1.
for all x > k where C = 12 and k = 1.
Hence,
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
109989
QUESTION_TEXT
Briefly explain 2 recursive functions with example.
Recursive theorem
SCHEME OF EVALUATION
Fibonacci sequence
GCD
(Any 2 of the above 5 marks each)