I have a question regarding buchi automatons. The automata for the LTL formula, G(Xa->b) is as the attached picture. Why dosen't a have to be true in order to make the automaton correct?
The formula states that for all $n$, if $a$ holds at time $n+1$ then $b$ holds at time $n$. If $a$ never holds then the formula is trivially true.