Question

What is the DFA of all strings starting with A and ending with B?

Answer 1

A DFA (Deterministic Finite Automaton) for all strings starting with 'A' and ending with 'B' can be constructed as follows:

1. Start with an initial state, which we'll call 'q0'.
2. Create two additional states: 'q1' and 'q2'.
3. From 'q0', create a transition labeled 'A' to 'q1'. This transition represents the requirement that the string must start with 'A'.
4. From 'q1', create a transition labeled 'B' to 'q2'. This transition represents the requirement that the string must end with 'B'.
5. From 'q2', create a self-loop transition labeled with any character, including 'A' and 'B'. This loop will allow the DFA to remain in 'q2' and accept any additional characters after 'B' if present.
6. Mark 'q2' as an accepting state since it represents a valid final state where the string ends with 'B'.

Here is a graphical representation of the DFA:

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