Question

If is a language, and is a symbol, then, the quotient of and, is the set of strings such that is in: is in. Suppose is regular, which of the following statements is true?

(a) L/a is always a regular language

(b) L/a is not a regular language

(c) All of the mentioned

(d) None of the mentioned

I have been asked this question in an internship interview.

The above asked question is from The NFA with n-moves to the DFA topic in portion Finite Automata and Regular Expression of Compiler

Answer 1

The correct choice is (a) L/a is always a regular language

Explanation: We can build a DFA for as such: firstly we get the DFA for: Then, we copy all the states and transitions to the DFA for. However, we mark any state as a final state in if and only if is a final state in.