NPTEL Theory of Computation Week 2 Assignment Answers 2024

NPTEL Theory of Computation Week 2 Assignment Answers 2024

1. Which of the following is equivalent to the set described by the regular expression 11^∗00^∗?

• {1^m0^m|m>0 is a natural number}
• {1^m0ⁿ|m,n>0 are natural numbers}
• {1^m0^m|m≥0 is a natural number}
• {1^m0ⁿ|m,n≥0 are natural numbers}

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2. Let L be a regular language. Then what can we say about the language
L′={a_na_n−1…a1∣n≥0,a₁a₂…a_n∈L}?

• L′ is regular
• L′ is not regular
• L′ may or may not be regular
• L′ cannot be generated by a regular expression

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3. Any regular expression of size n can be converted to an NFA (with ϵ -transitions) having at most (select the smallest possible asymptotic upper bound)

• O(n) states
• O(n2) states
• O(2n) states
• O(1) states

Answer :- 

4. Which of the following regular expressions generates the following language?
L={w∈{0,1}∗∣wbegins with 1 and ends with 0}

• 1(0+1)^∗0
• (10)^∗
• 1^∗0^∗
• 1(01)^∗0

Answer :- 

5. Which of the following regular expressions is equivalent to the regular expression (1+ϵ)(01)^∗(0+ϵ)?

• (0+ϵ)(01)^∗(1+ϵ)
• (1+ϵ)(10)^∗(0+ϵ)
• (0+ϵ)(10)^∗(1+ϵ)
• (01)^∗+(10)^∗

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6. Which of the following regular expressions generates the complement of the language generated the regular expression (00+11)^∗?

• (00+11)^∗(0+1)+(00+11)^∗(01+10)(0+1)^∗
• (00+11)(0+1)^∗+0(00)^∗+1(11)^∗
• (01+10)(0+1)^∗+0+1
• (00+11)(0+1)^∗+(0+1)(01+10)^∗

Answer :- 

7. Which of the following regular expressions generates the same language as the given DFA?

• (a(b+ϵ)(ba)^∗a+b(a+ϵ)(ab)^∗b)^∗
• ((b+ϵ)a(ab)^∗a+(a+ϵ)b(ba)^∗b)^∗
• ((b+ϵ)a(ba)^∗a+(a+ϵ)b(ab)^∗b)^∗
• (a(a+ϵ)(ba)^∗a+b(b+ϵ)(ab)^∗b)^∗

Answer :- 

8. Let R and S be two regular expressions. Which of the following is equivalent to the regular expression S(S+RS)^∗ ?

• R(SR+R)^∗
• (RR^∗S^∗S^∗)^∗
• (S+SR)^∗R
• RR∗S(RR^∗S)^∗

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