Prove that A={re {a,b)* | Each a in z is followed by at least one b) is regular.
Introduction:
To prove that the language A = {x ⋵ (a, b)* | Each a in x is followed by at least one b} is regular, we can construct a deterministic finite automaton (DFA) that accepts this language.
Let us build the DFA as follows:
Begin with the first state, q0.
Create a transition from the current state to the next state q1 for each input symbol a.
Create a transition from the current state to the next state q2 for each input symbol b.
Create a loop transition for input symbol b to return to the same state q1, and a transition for input symbol a to return to the initial state q0 for state q1.
Create a loop transition for input symbol b to return to the same state q2, and a transition for input symbol a to return to the beginning state q0 for state q2.
The last stage is q2, which supports the language A.
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