UPPCL AE 2018:26

Question

Which of the following languages over the alphabet $\Sigma = \{0,1\}$ is regular?

1. $0^{n} 1^{m}$
2. $0^{n} 1^{m}$ where $m=n+1$
3. $0^{m} 1^{n}$ where $m \equiv n(\text{mod 3}).$

 

• A. $\text{I}$ and $\text{III}$
• B. $\text{III}$ and $\text{II}$
• C. $\text{II}$ only
• D. $\text{III}$ only

Answer 1

case 1: Is regular because m and n can be any value so RE= 0*1* , we can draw a DFA so regual

case2: It is not regular the DFA cannot check the condition not even level 1 condition , we will need a PDF for this

case3: It is regualr as we can draw a DFA of this and it will require 3 states