# Automata Theory Questions and Answers – Operators of Regular Expression

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This set of Automata Theory Multiple Choice Questions & Answers (MCQs) focuses on “Operators of Regular Expression”.

1. A finite automaton accepts which type of language:
a) Type 0
b) Type 1
c) Type 2
d) Type 3

Explanation: Type 3 refers to Regular Languages which is accepted by a finite automaton.

2. Which among the following are incorrect regular identities?
a) εR=R
b) ε*=ε
c) Ф*=ε
d) RФ=R

Explanation: There are few identities over Regular Expressions which include: RФ=ФR=Ф≠R

3. Simplify the following regular expression:
ε+1*(011) *(1*(011) *) *
a) (1+011) *
b) (1*(011) *)
c) (1+(011) *) *
d) (1011) *

Explanation: ε+1*(011) *(1*(011) *) *
ε + RR*= ε + R*R= ε + R+= R*

4. P, O, R be regular expression over ∑, P is not ε, then
R=Q + RP has a unique solution:

a) Q*P
b) QP*
c) Q*P*
d) (P*O*) *

Explanation: The given statement is the Arden’s Theorem and it tends to have a unique solution as QP*.
Let P and Q be regular expressions,
R=Q+RP
R=Q+(Q+RP) P
R=Q+((Q+RP) +RP) +P=Q+QP+RPP+RPP=Q+QP+(Q+RP) PP+(Q+RP) PP=Q+QP+QPP+RPPP+QPP+RPPP,
If we do this recursively, we get:
R= QP*

5. Arden’s theorem is true for:
a) More than one initial states
b) Null transitions
c) Non-null transitions
d) None of the mentioned

Explanation: Arden’s theorem strictly assumes the following;
a) No null transitions in the transition diagrams
b) True for only single initial state

6. The difference between number of states with regular expression (a + b) and (a + b) * is:
a) 1
b) 2
c) 3
d) 0

Explanation:

7. In order to represent a regular expression, the first step to create the transition diagram is:
a) Create the NFA using Null moves
b) Null moves are not acceptable, thus should not be used
c) Predict the number of states to be used in order to construct the Regular expression
d) None of the mentioned

Explanation: Two steps are to be followed while converting a regular expression into a transition diagram:
a) Construct the NFA using null moves.
b) Remove the null transitions and convert it into its equivalent DFA.

8. (0+ε) (1+ε) represents
a) {0, 1, 01, ε}
b) {0, 1, ε}
c) {0, 1, 01 ,11, 00, 10, ε}
d) {0, 1}

Explanation: The regular expression is fragmented and the set of the strings eligible is formed. ‘+’ represents union while ‘.’ Represents concatenation.

9. The minimum number of states required to automate the following Regular Expression:
(1) *(01+10) (1) *
a) 4
b) 3
c) 2
d) 5

10. Regular Expression denote precisely the ________ of Regular Language.
a) Class
b) Power Set
c) Super Set
d) None of the mentioned 