1. Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________

a) reflexive

b) transitive

c) symmetric

d) reflexive and transitive

Explanation: A partially ordered relation refers to one which is Reflexive, Transitive and Antisymmetric.

2. The non- Kleene Star operation accepts the following string of finite length over set A = {0,1} | where string s contains even number of 0 and 1

a) 01,0011,010101

b) 0011,11001100

c) ε,0011,11001100

d) ε,0011,11001100

Explanation: The Kleene star of A, denoted by A*, is the set of all strings obtained by concatenating zero or more strings from A.

3. A regular language over an alphabet ∑ is one that cannot be obtained from the basic languages using the operation

a) Union

b) Concatenation

c) Kleene*

d) All of the mentioned

Explanation: Union, Intersection, Concatenation, Kleene*, Reverse are all the closure properties of Regular Language.

4. Statement 1: A Finite automata can be represented graphically; Statement 2: The nodes can be its states; Statement 3: The edges or arcs can be used for transitions

Hint: Nodes and Edges are for trees and forests too.

Which of the following make the correct combination?

a) Statement 1 is false but Statement 2 and 3 are correct

b) Statement 1 and 2 are correct while 3 is wrong

c) None of the mentioned statements are correct

d) All of the mentioned

Explanation: It is possible to represent a finite automaton graphically, with nodes for states, and arcs for transitions.

5. The minimum number of states required to recognize an octal number divisible by 3 are/is

a) 1

b) 3

c) 5

d) 7

Explanation: According to the question, minimum of 3 states are required to recognize an octal number divisible by 3.

6. Which of the following is not a part of 5-tuple finite automata?

a) Input alphabet

b) Transition function

c) Initial State

d) Output Alphabet

Explanation: A FA can be represented as FA = (Q, ∑, δ, q0, F) where Q=Finite Set of States, ∑=Finite Input Alphabet, δ=Transition Function, q0=Initial State, F=Final/Acceptance State).

7. If an Infinite language is passed to Machine M, the subsidiary which gives a finite solution to the infinite input tape is ______________

a) Compiler

b) Interpreter

c) Loader and Linkers

d) none of the mentioned

Explanation: A Compiler is used to give a finite solution to an infinite phenomenon. An example of an infinite phenomenon is Language C, etc.

8. The number of elements in the set for the Language L={xϵ(∑r) *|length if x is at most 2} and ∑={0,1} is _________

a) 7

b) 6

c) 8

d) 5

Explanation: ∑r = {1,0} and a Kleene* operation would lead to the following set=COUNT{ε,0,1,00,11,01,10} = 7.

9. For the following change of state in FA, which of the following codes is an incorrect option?

a) δ (m, 1) = n

b) δ (0, n) = m

c) δ (m,0) = ε

d) s: accept = false; cin >> char;

if char = "0" goto n;

Explanation: δ(QX∑) = Q1 is the correct representation of change of state. Here, δ is called the Transition function.

10. Given: ∑= {a, b}

L= {xϵ∑*|x is a string combination}

∑4 represents which among the following?

a) {aa, ab, ba, bb}

b) {aaaa, abab, ε, abaa, aabb}

c) {aaa, aab, aba, bbb}

d) All of the mentioned

Explanation: ∑* represents any combination of the given set while ∑x represents the set of combinations with length x where x ϵ I.