Question

Give a Regular Expression AND a DFA for the language L={w∈(a∪b)∗, w starts with a or ends with a}.

Answer 1

The Regular Expression for the language is 'a(a|b)* | (a|b)*a' and the DFA can be constructed with states and transitions to ensure strings start with 'a' or end with 'a'.

Step-by-step explanation:

The student is asking for a Regular Expression and a Deterministic Finite Automaton (DFA) for the language L, which includes all strings over the alphabet {a, b} that either start with an 'a' or end with an 'a'.

Regular Expression

The regular expression that satisfies the given conditions is a(a|b)* | (a|b)*a.

DFA

To construct a DFA that recognizes this language, we can follow these steps:

1. Create a start state that also serves as an accepting state, indicating that the string starts with 'a'.
2. Add a transition from the start state on input 'a' back to itself.
3. Add a second accepting state for strings that end with 'a'.
4. Add a transition from the start state on the input 'b', leading to a third state.
5. For the third state on input 'a', add a transition to the second accepting state.
6. For both the second accepting state and the third state, add transitions on input 'b' to the third state.
7. For the second accepting state, add a transition on input 'a' back to itself.

Following these steps ensures that the DFA will accept any string that either starts with or ends with 'a'.