Q#1
Write the Regular Expression of the language L that will accept any string consisting entirely of b's and will also accept any string in which the number of a's is divisible by 3. Also, make its Finite Automata and remember that the machine does not accept null, and the start and ending state cannot be the same. There is a clear representation of state numbers along with their signs and clearly represents the character that's transition is taking place. Also, label dead-end states properly.
Q#2
Consider a Language L that accepts all strings that have an odd number of occurrences of the substring abc over the alphabet = {ab.c}. Build a Finite Automata. There is a clear representation of state numbers along with their signs and clearly represents the character that's transition is taking place. Also, label dead-end states properly. Also, justify your Finite Automata that it accepts the given Language and rejects those strings which are not included in the above Language.
Hint: The final state can be more than one.